Classification of electroencephalogram (EEG) is a key approach to measure the rhythmic oscillations of neural activity, which is one of the core technologies of brain-computer interface systems (BCIs). However, extraction of the features from non-linear and non-stationary EEG signals is still a challenging task in current algorithms. With the development of artificial intelligence, various advanced algorithms have been proposed for signal classification in recent years. Among them, deep neural networks (DNNs) have become the most attractive type of method due to their end-to-end structure and powerful ability of automatic feature extraction. However, it is difficult to collect large-scale datasets in practical applications of BCIs, which may lead to overfitting or weak generalizability of the classifier. To address these issues, a promising technique has been proposed to improve the performance of the decoding model based on data augmentation (DA). In this article, we investigate recent studies and development of various DA strategies for EEG classification based on DNNs. The review consists of three parts: what kind of paradigms of EEG-based on BCIs are used, what types of DA methods are adopted to improve the DNN models, and what kind of accuracy can be obtained. Our survey summarizes the current practices and performance outcomes that aim to promote or guide the deployment of DA to EEG classification in future research and development. As a key tool to capture the intention of brain activity, electroencephalography (EEG) can be used to measure rhythmic oscillations of the brain and reflect the synchronized activity of substantial populations of neurons . The rhyDuring the execution of the interaction, the automatic classification of EEG is an important step toward making the use of BCI more practical in applications . HoweverIn the past few years, deep neural networks (DNNs) have achieved excellent results in the field of image, speech, and natural text processing . The feaOne promising approach is regularization , which cThe rest of the article is organized as follows. The search methods for identifying relevant studies is described in detail in section “Method.” In section “Results,” the basic concept and specific methods of DA in EEG classification based on DNNs are presented. Section “Discussion” discusses the current research status and challenges. Finally, conclusions are drawn in section “Conclusion.”A wide literature search from 2016 to 2021 was conducted through Web of Science, PubMed, and IEEE Xplore. The keywords used for the search contain DA, EEG, deep learning, DNNs. This review was conducted following PRISMA guidelines . ResultsData augmentation aims to prevent the overfitting of the DNN model by artificially generating new data based on existing training data . There aData augmentation based on image manipulations perform simple transformations using geometric features in an intuitive and low-cost way. Typical methods could be divided into the following categories.The geometric features of images are generally a visual representation of the physical information that contains both direction and contour elements . Common This method is realized by rotating the image along the horizontal or vertical axis under the premise that the size of the matrix was consistent.The operation of cropping can be realized by cropping the central patch of images randomly and then mixing the remaining parts.Data augmentation rotation is realized by rotating images along some coordinate axis. How to select rotation parameters is an important factor that affects the enhancement effect.Performing augmentations in the color channels’ space is another method to implement practically . During Color transformation realizes the generation of new data by adjusting the RGB matrix.Another approach to increase the diversity of data is injecting random matrices into the raw data, which are usually derived from Gaussian distributions .Augmentation methods by image manipulations perform the transformation in input space of data. However, these approaches cannot take advantage of underlying features of data to perform augmentation . RecentlAs shown in To obtain the expected generated data, a variational autoencoder (VAE) is proposed to improve the performance of the autoencoder. Compared with AE, VAE ensure that generated data is subject to specific probability distribution by adding constraints into the structure .2 represents variance, and ∈ is deviation.Where μ is the mean value of probability distribution, σGenerative adversarial networks refer to artificially generating data based on the principle of adversarial learning. As shown in p(x) is the distribution of training data and D is the discriminative model used to estimate the probability distribution p (•) between generated data z of real data x. V represents the value function and E is the expected value. In the process of training stage, the goal of GAN is to find the Nash equilibrium of a non-convex game with high-dimensional parameters. However, the optimization process of the model does not constraint for loss function that is easy to generate a meaningless output during the training stage. To address the issue and expand its application scope, the researchers proposed improved structures such as deep convolution GAN, conditional GANs, cycle GANs, and so on , visual evoked potentials (VEP), and event-related potentials (ERP). MI is a mental process that imitates motor intention without real output. Different imagery tasks can activate the corresponding region of the brain, while this activation can be reflected by various feature representations of EEG .Visual evoked potentials are continuous responses from the visual region when humans receive flashing visual stimuli . When exEvent-related potentials refers to a potential response when receiving specific stimulus such as visual, audio, or tactile stimulus .Compared with active BCI, passive BCI aims to output the EEG signals from subjects’ arbitrary brain activity, which is a form of BCI that does not rely on voluntary task .In this section, we review recent reports for DA in EEG classification based on DNNs.In recent years, scientific interest in the field of the application of DA for EEG classification has grown considerably. x(t) is recovered signal by EMD, IMF represents intrinsic mode functions, s represents the number of IMFs, and rs(t) is the final residual value. In the training stage, they mixed IMFs into the intrinsic mode functions to generate new data and then transformed it into tensors using complex Morlet wavelets which were finally input into a convolutional neural network (CNN). Experimental results verified that the artificial EEG frame could enhance the performance of the classifier and obtain higher accuracy.Where Pr and Pg are the distribution of real data xr and generated data xg. W represents the distance of two distributions and E is mean value. To improve the training stability and convergence, they utilized a gradient penalty to optimize the training process. Meanwhile, the proposed method addressed the problems of frequency artifacts and instability in the training process of DA. To evaluate the effectiveness of DA, they proposed two evaluation indices  to assess the quality of generated data. Experiments show that presentation-associated patterns of EEG could be seen clearly in generated data and they obtained significant improvement based on the EEGNet model after DA in the RSVP task (Where SVP task . A similn (1 < n < N) examples from the same category to calculate the average potential at each iteration, where N represents the number of all trials. RNN and CNN were used to classify different specific frequencies in the visual evoked potential (VEP) task and obtained significant improvement after DA.m nearest neighbors from the instance of the minority class and then adding these instances into real data by weighting calculation. The effectiveness of DA was evaluated by EEG data collected from the P300 task. Results show that the proposed methods could enhance the robustness of decision boundaries to improve the classification accuracy of P300 based on BCIs.Regarding EEG-based passive BCIs, they have gradually become more prominent in research , and areP is probability density function, and z is Gaussian random variable. xg is generated data after noise injection. There are three classification models, namely LeNet, ResNet, and SVM, that were used to evaluate the performance. Results show the generated data could significantly improve the performance for the classifier based on LeNet and ResNet. However, it obtains little effect on the SVM model.Where μ and σ are mean value and standard deviation, respectively, ELBO represent the evidence lower bound and xr and xg is real data and generated data, respectively. The goal of optimization was to maximize ELBO which was equal to minimizing the KL divergence between the real data and generated data. Based on the loss function of GAN, an extra penalty term is added to it:Where 2 is 2-norm value. In their work, the training samples of DA models were transformed into the forms of power spectral density or differential entropy and the performance of different classifiers are compared after DA. Experiments show that two representations of EEG signals were suitable for the requirement of the artificial datasets that enhances the performance of the classifier.Where λ is weight coefficient for the trade-off between the original objective and gradient penalty, and To comprehensively show the implementation, we summarize the details of the application of DA in EEG decoding in The limitation of small-scale datasets hinders the application of DL for EEG classification. Recently, the strategy of DA has received widespread attention and is employed to improve the performance of DNNs. However, there remain several issues worth discussing.Taking the above discussion into consideration, we found that the input forms of DA models could be divided into three categories: time-series data, spectral image, and feature matrix. We also found that researchers preferred to convert EEG signals into image signals for subsequent processing in MI tasks. One possible reason might be that the features of MI are often accompanied by changes in frequency band energy, i.e., event-related desynchronization (ERD)/event-related synchronization ERS; . This phFrom a difference of implementation point of view, DA can be divided into input space augmentation and feature space augmentation. Indeed, the former aspect has the advantage of interpretability and takes lower computational costs. However, we found that the operation in feature space could obtain more significant improvements than in input space based on the results of classification performance presented in Generative adversarial networks have become popular for generating EEG signals in recent years , althougPrevious studies show that DA could improve the decoding accuracy of EEG to varying degrees in different EEG tasks. However, this improvement varies greatly in different data sets and preprocessing modes. There are several possible explanations to be discussed. First, most studies have not discussed whether DA produces negative effects in the training stage of the classifier. As mentioned in the above discussion, EEG signals are accompanied by strong noise and multi-scale artifact. But existing DA methods are global operations, which cannot effectively distinguish these irrelevant components. Meanwhile, EEG signals collected from specific BCI tasks  perform features that are time-locked and phase-locked, which may cause wrong feature representation using GT to produce artificial data. While GT performs effectively in MI and ER tasks due to this kind of signal having no strict requirement for feature-locking. Therefore, feature representation of EEG should be analyzed before the application of GT. Second, there are a few studies that discuss the boundary conditions of the feature distribution for generated data, even though it is one of the important guarantees of data validity.Another important issue worthy to discuss is how much generated data could most effectively enhance the performance of a classifier. Researchers have explored the influence of different ratios of real data (RD) and generated data (GD) for classification performance and demonstrated that the enhancement effect does not increase with the size of GD . ResearcBased on the above analysis we believe that the following studies are worthy of exploring in further research. First, different DA methods can be combined to extend datasets and augmentation would be executed both in input space and feature space. For example, generated data based on GT can be put into GANs to realize secondary augmentation, which may improve the diversity of generated data. Second, combining meta-learning with data enhancement might reveal why DA affects classification tasks, which may improve the interpretability of generated data. Meanwhile, DA based on GAN is a mainstream method at present, but how to improve the quality of generated data is still a valuable point.Collecting large-scale EEG datasets is a difficult task due to the limitations of available subjects, experiment time, and operation complexity. Data augmentation has proven to be a promising approach to avoid overfitting and improve the performance of DNNs. Consequently, the research state of DA for EEG decoding based on DNNs is discussed in the study. The latest studies in the past 5 years have been discussed and analyzed in this work. Based on the analysis of their results, we could conclude that DA is able to effectively improve the performance in EEG decoding tasks. This review presents the current practical suggestions and performance outcomes. It may provide guidance and help for EEG research and assist the field to produce high-quality, reproducible results.CH is responsible for manuscript writing. JL draw related figure. YZ and WD guide the literature collection and structure of the manuscript. All authors contributed to the article and approved the submitted version.CH and JL were employed by the company Shenzhen EEGSmart Technology Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Tumors involving the hard palate, maxillary sinus, or nasal cavity require maxillectomy based on the extent of the lesion. Lack of these boundaries affects the speech, esthetics, and masticatory function. Prosthetic rehabilitation of these defects can be done utilizing zygomatic implants. This present case describes the use of a zygomatic implant to retain a maxillary obturator in a 22-year-old male patient following partial maxillectomy (Brown's Class 2b) due to odontogenic myxoma. A surgical obturator was secured in position subsequent to the implant placement. Following the healing period, an interim obturator using heat cure acrylic was fabricated. Mechanical retention for the definitive obturator was obtained through the ball attachment suspended from the multiunit abutment of the zygomatic implant. The case was followed up closely for a year to evaluate the function of the prosthesis. The prosthetic rehabilitation not only promoted esthetics and function but also improved the patient's quality of life. A challenging endeavor for prosthodontists is rehabilitating patients with maxillectomy/atrophic maxilla as it is a complex area. Carcinomas involving the hard palate, maxillary sinus, and nasal cavity will require maxillectomy, causing dysfunction of the stomatognathic system and thus affecting the patients' quality of life . Tumors A custom-made dental prosthesis such as an obturator plays an important role to promote function and esthetics and helps in maintaining the oro-nasal separation. Obtaining retention and stability depends on the extent of the defect, the remaining number of natural teeth, the amount of residual bone, and the patients' ability to adapt to the prosthesis . UsuallyThis clinical report describes the successful management of a patient with maxillary odontogenic myxoma who underwent partial maxillary resection followed by prosthesis using a zygomatic implant.A 22-year-old male patient was referred to Rajarajeswari Dental College and Hospital with a complaint of swelling in the left maxillary posterior region. On extraoral examination, no gross facial asymmetry was noticed. Intraorally, there was no pain/mobility of the teeth. The swelling extended from 23 to 26 region as shown in Through the intraoral approach, partial maxillectomy was carried out by preserving the frontal wall of the maxillary antrum, zygoma, and the floor of the orbit. The anterior cut was undertaken through the left lateral incisor and limiting the posterior cut up to the 1st molar as seen in After 4 weeks of the healing period, the patient was recalled for the fabrication of an interim obturator. There was no evidence of infection with good healing of the soft tissues around the abutment as seen in Five months following the surgery, a fixed-removable prosthesis was planned by utilizing precision attachments. The diagnostic casts were mounted on a semiadjustable articulator following a face bow transfer, and the amount of space available for the attachment was evaluated using a putty index. As the available space was more than required (15 mm), a ball and socket attachment system was planned with a cast partial denture. Occlusal rest seats were prepared on 15 and 16 to receive an embrasure clasp, and the guide planes were prepared on 21 and 27, respectively. Following mouth preparation, a custom tray was fabricated to make an abutment level impression using heavy and light body consistency of polyvinyl siloxane impression material as seen in Various procedures such as obturators, local flaps, and microvascular flaps have been advocated to reconstruct the maxilla following the surgical resection –13. MicrThe amount of remaining horizontal component is the deciding factor in restoring the subjects with an obturator. A significant amount of forces can be distributed on the remaining dentition through clasps to retain the prosthesis in position . Due to Apart from this, there are certain complications associated with the placement of zygomatic implants, such as orbital injury/penetration, oroantral fistula formation, sensory nerve deficits temporarily, and vestibular cortical fenestration . To overZygomatic implants have proven to be an alternative to the traditional methods in restoring subjects with maxillectomy defects as they help in retaining the obturators. With a proper diagnosis and treatment plan, a multidisciplinary approach involving a radiologist, surgeon, and prosthodontist helps to reconstruct and rehabilitate at various stages of treatment. The ultimate goal of the clinician is to improve the quality of life of the patient.


Hernias through a defect of the broad ligament are rare, accounting for only 1.6–5% of internal herniations A 78-year-old multiparous woman presented with lower abdominal pain and nausea. Contrast-enhanced multi-detector CT (MDCT) demonstrated a dilated sigmoid colon and edematous mesentery of the sigmoid colon in the left Douglas' fossa, the uterus was compressed dorsally to the right and the left ovary was compressed ventrally. We diagnosed an internal broad ligament defect hernia with incarceration of the sigmoid colon, and performed emergency laparotomy. The necrotic sigmoid colon was resected and anastomosis was performed by the double stapling technique. The postoperative course was uneventful.We consider the treatment of hernia of sigmoid colon through a broad ligament defect.We recognize that there is a possibility that, in addition to the small intestine, proximally located organs may be incarcerated. In the case of the colon, we should choose the treatment method carefully according to whether or not the colon is expected to be necrotic. •Hernia of the sigmoid colon through a broad ligament defect is rare.•The approach is based on whether or not the sigmoid colon is necrotic.•We can evaluate whether it is necrotic or not and reposition by colonoscopy.•Anatomically proximal organs may be incarcerated through such defects. Contrast-enhanced MDCT showed on the one hand a dilated sigmoid colon and edematous mesentery of the sigmoid colon in Douglas' fossa with ascites collection, on the other hand there was no dilatation of the small intestine or air fluid level in the small intestine. The uterus was compressed to the right dorsally and the left ovary was compressed ventrally (A 78-year-old multi-parous woman consulted her family doctor of lower abdominal pain and nausea, and was admitted to our hospital the following morning. There is no relevant past, surgical or family history, and she was not using any chronic medication. On physical examination, the abdomen was diffusely tender with no guarding or increased bowel sounds. Her vital signs were stable. Laboratory findings showed no definite abnormalities, with the exception of a slightly elevated white blood cell count (10,900/mmentrally A, B, C.FFrom these findings, we diagnosed an internal broad ligament defect hernia with incarceration of the sigmoid colon and performed emergency laparotomy without the transnasal drainage tube. A 15-cm loop of sigmoid colon had incarcerated by the left suspensory ligament of the ovary through a 3-cm defect of the left broad ligament in a ventral to dorsal direction and the sigmoid colon had become necrotic. The left suspensory ligament of the ovary and the left ovarian artery and vein were dissected and the left ovary was excised A, B. The3The defect is classified into 2 types: the fenestra type in which the anterior and posterior layer of the broad ligament are penetrated; and the pouch type, in which either the anterior or posterior leaf is penetrated and a blind pouch is formed CT is useful for the diagnosis of hernias through broad ligament defects In most cases involving incarcerated hernia through a broad ligament defect, the incarcerated organ is the small intestine, incarceration of the sigmoid colon is rare. Kawai et al. In recent years, the number of reports describing the laparoscopic treatment of hernia through broad ligament defects has increased In this case, instead of a laparoscopic approach, we chose to perform emergency laparotomy without the above-described preoperative procedure because we suspected necrosis of the sigmoid colon and visibility is expected to be poor due to dilatation of the sigmoid colon. In cases of hernia of the sigmoid colon, which is different from the small intestine, we should choose the treatment method carefully, it is difficult to maintain sufficient working space in the presence of the dilated bowels because mobility of the colon is limited in comparison to the small intestine and because preoperative transnasal drainage of the intestine has often no immediate effectivity or effort for the colon. Furthermore, when the bowel is necrotic, the risk of perforation and intraperitoneal contamination is higher.4To facilitate an early diagnosis, hernia through a defect of the broad ligament should be added to the list of differential diagnoses of female acute abdomen and it should be considered that in addition to the small intestine, proximally located organs may be incarcerated. In the case of the incarceration of the colon, we should choose the treatment method carefully according to whether or not the colon is expected to be necrotic.This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.This report was reviewed and approved by the Institutional Review Board of Gifu Prefectural General Medical Center.Informed consent was obtained from the patient for publication of this case report.Shinya Ohno: Data Acquisition, Data Interpret and writing of the manuscript.Wakana Chikaishi & Takuya Sugimoto: management of case.Shuji Komori: Supervision, review and editing.Masahiko Kawai: Supervision, review, editing, and final approval of the version to be submitted.Not applicable.The guarantor is Shinya Ohno.Not commissioned, externally peer-reviewed.The authors declare no conflicts of interest.


Pneumonia is a highly transmitted disease in children. According to the World Health Organization (WHO), the most affected regions include South Asia and sub-Saharan Africa. 15% deaths of children are due to pneumonia. In 2017, 0.88 million children were killed under the age of five years. An analysis of pneumonia disease is performed with the help of a delayed mathematical modelling technique. The epidemiological system contemplates subpopulations of susceptible, carriers, infected and recovered individuals, along with nonlinear interactions between the members of those subpopulations. The positivity and the boundedness of the ongoing problem for nonnegative initial data are thoroughly proved. The system possesses pneumonia-free and pneumonia existing equilibrium points, whose stability is studied rigorously. Moreover, the numerical simulations confirm the validity of these theoretical results. In 2014, Mochan et al. presented the interhost immune response to bacterial pneumonia infection in murine strains in a simple ordinary differential equation model dynamically . KosasihPneumonia is a terrible strain in developing regions such as Asia, Africa and Europe. Pneumonia vaccination has been introduced in developed countries, and even the United States is the largest donor for nefarious purposes. Delay modelling is a more general form of deterministic modelling. The delayed analysis is a more realistic, close nature and authentic tool to control infectious diseases. For example, in the recent strain of coronavirus, the only control strategy is delaying tactics like public holidays, restriction in travel, facemask, hand sanitiser, social distancing etc. This article claims that precautionary measures or delay tactics are the best revenge to control pneumonia-like diseases other than vaccination or medication etc. That is a reason why we move in delay modelling.The paper strategy is as follows: Sect. Newly recruited individuals are assumed to be in the susceptible class.The birth and death rates are approximately equal.Vertical transmission is to be considered.Susceptible types make attraction with the infected and carriers classes at any time Natural delay is assumed.An artificial delay term like Once recovered, they may have chances to get the disease again.The carriers may recover directly due to their internal immunity.The carriers and infected classes have inverse interactions with each other.Two types of death rates are considered: natural and due to the disease.The formulation of the model is based on the theory of population dynamics. The population mentclass2pt{minimTable Based on the assumptions, the continuous model is defined with the help of the law of mass action. The nonlinear delay differential equations (DDEs) present the transmission flow of pneumonia type diseases as follows: To preserve the meaningful analysis of the model, all the variables The solutionsof system  is a is a4) iSince all the parameters and derivatives of the model are nonnegative, system –4) admi admi4) aThe solutionsof system  and  and 4) aThe pneumonia trivial equilibrium  in t in t4) iThe pneumonia trivial equilibrium In this section, we have taken the effect of system –4) with with4) w(Behavior of reproduction number with the efficiency of delay tactics)In Fig. Fig. (D-simulations of the system)2D graphics are widely used in animation, providing a realistic but flat view of movement on the screen. We plotted the two-dimensional performance of the model with different subclasses for a better interpretation of the dynamics of pneumonia disease, as presented in Fig. In this article, we investigated the mathematical analysis of pneumonia delayed epidemic models with reliable delay strategies. The model is based on four types of subpopulations like the susceptible, the carriers, the infected and the recovered. Dynamical analysis of the model includes positivity, boundedness, equilibria and threshold parameter. The sensitivity of the parameters is one of the outcomes of the model. Linearisation of the model is developed by well-known results like the Jacobian and Routh–Hurwitz criterion. Lyapunov theory and the Lassale invariance principle are investigated for the global stability of the model. The following artificial control measures could support the eradication of the disease in the population: the cleanness of hands, extensive use of fruits and vegetables, calm sleeping, staying away from smoking, vaccination to the children under five years and being aware of your general health.


Bovine viral diarrhea virus (BVDV) is an economically important disease in Australian beef farming. The disease typically results in low-level production losses that can be difficult to detect for several years. Simulation modeling can be used to support the decision to control BVDV; however, current BVDV simulation models do not adequately reflect the extensive farming environment of Australian beef production. Therefore, the objective of this study was to develop a disease simulation model to explore the impact of BVDV on beef cattle production in south-east Australia. A dynamic, individual-based, stochastic, discrete-time simulation model was created to simulate within-herd transmission of BVDV in a seasonal, self-replacing beef herd. We used the model to simulate the effect of herd size and BVDV introduction time on disease transmission and assessed the short- and long-term impact of BVDV on production outputs that influence the economic performance of beef farms. We found that BVDV can become established in a herd after a single PI introduction in 60% of cases, most frequently associated with the breeding period. The initial impact of BVDV will be more severe in smaller herds, although self-elimination is more likely in small herds than in larger herds, in which there is a 23% chance that the virus can persist for >15 years following a single incursion in a herd with 800 breeders. The number and weight of steers sold was reduced in the presence of BVDV and the results demonstrated that repeat incursions exacerbate long-term production losses, even when annual losses appear marginal. This model reflects the short- and long-term production losses attributed to BVDV in beef herds in southeast Australia and provides a foundation from which the influence and economic utility of BVDV prevention in Australian beef herds can be assessed. Endemic diseases are responsible for significant economic losses in the Australian beef industry. A report commissioned in 2015 indicated that bovine viral diarrhea virus (BVDV) was the second-most economically significant endemic disease affecting Australian beef production . A revieLoss of production in beef herds is typically characterized by the reproductive effects of BVDV. Early embryonic death and abortion as a result of virus exposure can lead to reduced pregnancy rates and increased calving intervals . This efIn a herd with endemic BVDV infection, the reproductive and immunosuppressive effects of the disease typically result in low-level annual production losses which can be difficult to detect, but the loss over several years can be significant . The proDespite these interventions, the success of nationwide control of BVDV is highly variable and modeling has been used to study country-specific disease dynamics and facilitate decisions for disease control . DiseaseSimulation models have been used to assess the effect of BVDV in beef herds in Scotland, Ireland, United States and France –24. ThesThe objective of this study was to develop a disease simulation model to investigate the impact of BVDV on Australian beef farms and inform the need for intervention in environments typical of beef farming in southeast Australia. The study compares the short- and long-term impacts of BVDV on beef production to highlight the production losses that can occur in the absence of disease prevention strategies.A dynamic, individual-based, stochastic discrete-time simulation model was created using the software R  to assesOn each day of the simulation (one time-step), the model was updated in five stages: (1) disease transmission; (2) movements between groups on the farm; (3) removal of animals ; (4) pregnancy status; and (5) addition of animals (through purchases or births). Model parameters including herd structure and contact rates are described below. A Bernoulli process was used to model stochasticity for the probability of daily infection, mortality risk, probability of conception and daily probability of abortions. Sensitivity analysis was conducted to assess the influence of model parameters on the outputs of interest, as described below.The herd consisted of bulls (B), cull cows (CC), weaned steers (WS), weaned heifers (WH), first-calving cows (FC) and mature cows (MC). Each animal group was assigned to a single virtual paddock  with the exception of MCs, which were split into age-related groups (≥ Paddock 6). The maximum number of MC paddocks was based on the bull-to-cow ratio and varied according to breeding herd size .Any WH that was not pregnant at day 126 following the end of the breeding period (simulated pregnancy testing) was culled from the herd . FC and A CF was added to the herd when the gestation counter was equal to the breeding animal's assigned gestation period, signifying the end of gestation. In the absence of BVDV, a BVDV-susceptible, healthy calf was produced with a 0.5 probability of being male . The estvia aerosols, vectors or fomites between groups  is described by equation 1:When accounting for all routes of transmission of BVDV, the daily risk of infection for an individual animal in group *For animals involved in management practices on that day.IPIj = the number of persistently infected animals within paddock j; pPI = the probability of daily effective contact between individuals for PI transmission within paddock j; ITIj = the number of transiently infected animals within paddock j; pTI = the probability of daily effective contact between individuals for TI transmission within paddock j; IPIk= the number of persistently infected animals in paddock k; pPIk = the probability of daily effective contact from PI animals in paddock k to animals in paddock j . IPIh and ITIh represent the number of PI animals and the number of TI animals involved in a health management practice, respectively. The value for pPI in the current model study was derived from values used in Han, Weston  was derived from the relationship between risks and rates as described by Vynnycky and White . The mortality rates of adult cattle and healthy calves were derived from industry data from Meat & Livestock Australia  , 54, 55.The model simulated live weight gain for CF, WS, WH and FC. Daily weight gain was calculated as an animal-specific percentage of individual animal live weight, derived from industry standard targets . Calves An outbreak of BVDV on a beef herd in central Queensland Australia recorded significant variability in the weight of PI grower steers at weaning and sale . There iSimulations commenced at the start of joining and prior to each scenario  the modeIn Scenario 1, a single animal (<3 years old) was randomly selected and converted to a PI animal to simulate introduction of a PI animal into the farm from an external source. The model was run for a simulation period of 15 years with no further introduction of the virus. The day of BVDV introduction was recorded and categorized according to the time of year . ScenariScenario 2 and 3 examined the impact of BVDV introduction frequency by simulating the introduction of a PI animal at regular intervals over a 15-year period . As withModel outputs of interest were those that contribute to the economic performance of an Australian beef herd, including: the number of heifers retained for breeding, the number of cows culled, the number of bulls purchased, the annual number of steers sold and the number of those steers that were under the target weight to obtain a premium price at sale . It is aPI animals are the main contributors to BVDV transmission and persistence within a herd. Therefore, if a PI animal was born following disease introduction, we characterized this as establishment of infection within the herd. Self-elimination of the virus was classified as the last year that any infected animals  were present in the herd. The cumulative number of infected (TI and PI) animals was also of interest in those scenarios with BVDV transmission. Simulations were repeated for all scenarios until the model outputs reached convergence, with input variables changing every iteration according to the distributions in The effect of disease introduction frequency on performance was also demonstrated by taking the “per breeding animal” difference in outputs from Scenarios 1–3 compared to Scenario 0, at the cumulative 5-, 10- and 15-year values for all outputs of interest to enable direct comparisons between herd sizes.Internal validation of the model was achieved using the rationalism and the tracing methods . ImplemeExternal validation was achieved by comparing the model outputs to published data from the BVDV literature. Transmission characteristics of the virus and model outputs such as pregnancy risk, abortion rate and calf deaths were validated against corresponding values from Australian BVDV outbreaks using the modeling scenario, breeding herd size and introduction time that best fit the context of published cases.The number of iterations required to achieve convergence for each modeling scenario was identified using the method described in Brookes et al. . BrieflySensitivity analysis was used to determine the influence of input variables on the outputs of the scenario with the most variation (as determined by convergence testing). Only input variables that changed with every iteration of the model (based on a uniform or PERT distribution) were included in the analysis, as well as breeding herd size and introduction time . CollineScatter plots were used to assess for collinearity between input parameters. Generalized additive mixed models  with a The outcome of convergence testing for all scenarios is illustrated in n = 2983) of all iterations following a single PI introduction and therefore, quantitative analysis of all results that follow are based on these iterations. BVDV was least likely to become established in a herd with 50 breeders and after an incursion at Introduction Time 3 (BVDV became established in 59.66% (n Time 3 . The maxn Time 3 . The maxn Time 3 .n = 2739) of cases (*No self-elimination occurred in the upper 95% percentile), respectively  per breeder over five years. Of these steers, median 0.015 steers/breeding animal (95% range −0.130 to 0.155) had liveweight at sale insufficient to reach the premium price range. The number of cows culled from the herd was also affected by BVDV, but to a lesser extent than steer sales . CompareA description of the model outputs and reference values used for external validation of the model are summarized in Sensitivity analysis was conducted using Scenario 1 (most variation in model outputs). Scatter plots indicated no evidence of collinearity and so all parameters in The individual producer is solely responsible for the prevention and control of BVDV in Australia. This novel disease simulation model reflects the impact of BVDV in settings consistent with Australian beef production at the individual farm level. Convergence testing demonstrated stability in all of the model outputs, illustrating little variation between simulations. Model outputs indicated that a single BVDV incursion is likely to cause the birth of at least one PI animal (meaning that infection is established in the herd) in ~60% of all simulations. The timing of BVDV introduction in relation to the production calendar had the most influence on establishment, which was most likely for the 73 days prior to joining through to 146 days after the joining period. This is recognized as the highest risk period for persistent infection in developing fetuses , 69, 70.Once BVDV has become established in a beef herd, the model demonstrates that herd size characterizes the severity and length of the outbreak. The proportion of animals in the simulated farm that were viremic at the peak of infection had an inverse relationship to breeding herd size; however, the distribution of MCs in simulated paddocks may have contributed to these results. The number of MCs in each paddock is fixed in this model, based on the bull-to-cow ratio. Smaller herds will have a higher proportion of breeding animals in a single paddock when compared to a large herd, in which the breeding herd is spread across multiple paddocks. BVDV transmission within a paddock will initially result in a higher proportion of infected animals in a smaller herd. Transmission within a paddock diminishes over time as animals become immune to infection and so, transmission between paddocks becomes responsible for BVDV persistence within the farm. Therefore, the duration of a BVDV outbreak in the model increased as herd size increased. A herd of 50-breeders had a maximum outbreak duration of 8 years following a single introduction, compared to an 800-breeder herd, in which 23% of outbreaks continued after 15 years. In reality, it is reasonable to assume that larger farms would consist of more paddocks than those with smaller herds to achieve ideal stocking rates to maximize production . The relvia breeding stock. It was not possible to ascertain the infection status of these animals retrospectively, and it is possible that introduction of multiple infected animals may have contributed to a longer time to elimination. In addition to elimination time, data from the model for the 400-breeder herd showed that the 2-and 4-year seroprevalence in the 73-day period prior to joining were comparable to the values reported by Allworth et al. (While the median duration of BVDV outbreak in the simulated 400-breeder herd (4 years) was shorter than that reported for a similar sized Australian outbreak, the 95% range included the published values for elimination time . In theh et al. . The modh et al. . These eDairy, intensive beef and extensive beef farming operations require different approaches to BVDV detection and prevention as a result of variations in farm management , 69, 72.Long et al.  found thA limitation of this model is an inability to account for the impact of secondary infections that may exacerbate the effects of BVDV. Immunosuppression is a documented consequence of BVDV infection that is suggested to facilitate secondary infections that may increase abortion, calf mortality and reduce growth performance –81. In tUsing simulation modeling, this study described the impact of BVDV on a farm characteristic of Australian beef farming. Exposure to BVDV is most likely to cause an outbreak when the virus is introduced in conjunction with the breeding period and there is a high (60%) likelihood that BVDV will be established in a beef herd after the introduction of a single PI animal. The initial impact of a BVDV outbreak will be more severe in smaller beef herds; however, the virus takes longer to self-eliminate as herd size increases. The model can measure the underlying production losses that can occur from long-term outbreaks of BVDV which might otherwise go unnoticed in the field; however, economic analysis is required to determine the financial implications of BVDV in Australian beef production. Future studies can use this model to investigate BVDV prevention strategies for Australian beef farms.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The study was designed by JF, VB, MH-J, JM and YM as part of a PhD project. Modeling and data analysis were performed by JF, with assistance from VB, CK, and TH. All authors read and approved the final manuscript.This study is part of a PhD project that was supported by an Australian Research Training Program (ARTP) scholarship, with a top-up from the Graham Centre for Agricultural Innovation and Meat and Livestock Australia Ltd. There was no involvement of the funding sources in the study design, collection or analysis of data, interpretation of results, or the decision to submit the article for publication.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Population aging poses challenges to the immature elderly care service system in many countries. The strategic behaviors of different participants in the provision of elderly care services in a long-term and dynamic situation have not been well studied. In this paper, an evolutionary game model is developed to analyze the strategic behaviors of two types of participants—the government sectors and the private sectors in provision of elderly care services. Firstly, eight scenarios are analyzed, and the evolutionary process and stable strategies are identified. Then, the behavioral strategies of the two types of participants under demand disturbance and dynamic subsidy strategy are analyzed. Simulation experiments are conducted to explore the influence of different initial conditions and parameter changes on the evolutionary process and results. The obtained observations are not only conducive to a systematic understanding of the long-term dynamic provision of elderly care services but also to the policymaking of the government. Data from the United Nations show that there are 702.9 million individuals aged over 65 worldwide in 2019, which is expected to increase to 1.55 billion by 2050 . TherefoThe elderly people often suffer from chronic diseases, disability, or semi-disability . ImperfeThe issues of elderly care services have attracted attention from many scholars. Existing studies of elderly care services are mainly focused on qualitative analysis of policies and current situations of elderly care services ,10, empiAt present, many scholars have studied the optimal provision strategy of elderly care services in a one-time transaction ,13,14. HThis research aims to study the decision-making process of government sectors and private sectors in the provision of elderly care services in a long-term and dynamic environment. We establish an evolutionary game model to analyze the provision decision of elderly care services with considering that the participants are not completely rational in the long-term decision-making process. Through the analysis of evolutionary game model, we obtain the evolutionary equilibriums of the system under different scenarios, the impacts of different parameters on the evolutionary process and results, and the impacts on the elderly care provision system when facing the changes in environment and policy-making. By systematically analyzing the decision-making process under different scenarios and changes, we obtain relevant management implications to help the policy making of government sectors in elderly care service system. As far as we know, there is no existing research analyzing the decision-making of the government sectors and private sectors in the provision of elderly care services from such a perspective. This research fills this gap and tries to answer the following research questions:(1) In the long-term and dynamic provision process of elderly care services, the government sectors can adjust the supervision intensity of the private sectors, and the private sectors can set the level of services provided. What supervision strategies do the government sectors adopt under different conditions? Under what conditions are the private sectors willing to deliver high-quality services?If the subsidy, fine, or supervision cost of government sectors is adjusted, or the cost of private sectors is changed, how will the decisions of the private sectors be affected?If there is disturbance in service demand within a long period of time, how will the decisions of the two types of participants be affected? Moreover, if the government sectors adopt a dynamic subsidy policy, how will it affect the decisions of the participants?(2) What effect will it have on the decisions of the government sectors and the private sectors if there are the following changes in the long-term provision process of elderly care services:(3) What policies and measures should the government sectors take to encourage the private sectors to provide high-quality services for the elderly?The rest of this paper is structured as follows. In This research mainly relates to two literature streams. From the perspective of the research problem, it is related to elderly care services and its provision. On the other hand, from the modeling perspective, it is related to the EGT and its application.Problems and challenges faced in the provision process of elderly care services have raised the attention of many researchers. Take China as an example, the involvement of private sectors in the provision of elderly care services is increasing while the shortage of long-term care staff and the poor quality of services are worrying. The shortage of care beds is also an urgent problem; China has about half as many long-term care beds per 1000 elderly people as most developed countries do . MoreoveGame theoretic approaches can provide a quantitative decision framework for modeling, analyzing as well as predicting the behaviors of the players in the game . As is wRecently, EGT has attracted attention from researchers for solving economic and social problems . For insFrom the above-cited studies, we can see that existing studies on elderly care services mainly focused on policy research, qualitative analysis, and empirical analysis. Although there are some papers on quantitative analysis of the provision of elderly care services, they all focused on the optimal provision strategies, but ignored the impacts of the change in participants’ behavior strategies, the interaction between participants, as well as the change of environmental and other related factors to the elderly care services provision process. Based on the analysis above, we believe that the EGT is more suitable for us to analyze the long-term provision process of elderly care services. To the best of our knowledge, there is no research using EGT to analyze the behavior strategies of the government and the private sector in the provision of elderly care services. As such, we develop an evolutionary game model to analyze the behavior strategies of government sectors and private sectors in the provision process of elderly care services under different situations.In the following, we take China as an example to describe the decision problem. The government has built up a dual system of institutional elder care: one is managed and owned by the government; the other is market driven and run by the private sectors . The govBased on the analysis of the actual situations, we formulate the behaviors of the government sectors and the private sectors in the provision of elderly care services as an evolutionary game. The model is described in detail as follows.To facilitate modeling, we present the following assumptions:(1) There are two types of participants in the provision process of elderly care services—the government sectors and the private sectors. Similar settings can be found in Li et al. (2016) .(2) Each of the two types of participants has two strategies to choose from. The government sectors have two types of choices: implement supervision and implement no supervision. It costs (3) Both of the two types of participants are with bounded rationality. Because of incomplete information, they have limited abilities in rational cognition and decision-making. However, each entity of a type of participants may interact with each other and can learn constantly to adjust its strategy .(4) Provision of high-quality elderly care services brings a positive reputation benefit to the government sectors, which we defined as . (2020) .(5) Many elderly people are suffering from long-term chronic diseases; they are at higher risks of sudden illness and accidents. Hence, we assume that the private sectors providing low-quality services face a risk cost, For the government sectors, it is necessary to formulate reasonable policy on the provision of elderly care services and regulate the behavior of private sectors. Moreover, elderly care services have the characteristics of high investment costs, long return cycles, and low profit, hence the government sectors need to make supporting policies for the private sectors while regulating them. The private sectors are the direct providers of elderly care services. It is unrealistic to achieve high-quality service provision only by the self-discipline of the private sectors without supervision of the government. Therefore, the supervision strategy should be the dominating strategy of the government sectors, and for the provision of elderly care services, supervision strategy, and high-quality services are ideal decision-making results. The private sectors can get a per capita subsidy from the government sectors. However, when the private sectors provide low-quality services while the government sectors implement supervision, the private sectors will be punished by the government and receive no subsidy, the government will compensate the customers in the meanwhile. The two types of participants pursue social value or economic value in the provision process of elderly care services. For the sake of analysis, we express it as fitness here.The main notations of the model and their definitions are listed in R) and its supervision (K). Moreover, the government sectors have to pay for the supervision cost (S) and the subsidy (F) from the private sectors, while pay for the supervision cost (S) and the subsidies to the customers (M) who receive low-quality services, corresponding to The game players have different strategies and payoffs. The pure strategies of the government sectors are: (1) Is: the government sectors implement supervision; (2) Ns: the government sectors implement non-supervision. The pure strategies of the private sectors are: (1) Hs: the private sectors provide high-quality services; (2) Ls: the private sectors provide low-quality services. According to the assumptions above, when the government sectors choose Is and the private sectors choose Hs, the government sectors obtain positive revenue from the high-quality services (We thus obtain the expected return of the government sectors. If the government sectors choose to implement supervision (non-supervision), the payoff function is The replicator dynamic equation can be used to describe the evolution of participants’ strategy over time. In a replicator dynamic system, the growth rate of a strategy is equal to the difference between its fitness and population average fitness . TherefoSimilarly, we obtain the replicator dynamic equation of the private sectors providing high-quality services:Equations (4) and (5) constitute the replicator dynamic system for the provision of elderly care services.To simplify the expressions, we define the following four expressions, From the above replicator dynamic system, we obtain the following proposition.Proposition 1.For the replicator dynamic system of elderly care services provision given by Equations (4) and (5), we have:(i) Fixed points , , , and  are the equilibriums of the system.(ii) See the The equilibrium depends on the ratio of participants’ initial strategies and the sign symbol of the differential equation in corresponding interval . Accordis an ESS . We exprThen, The expressions of We get eight scenarios according to the sign symbol of Friedman , we obtaScenario 1.When Scenario 2.When Scenario 3.When Scenario 4.When The phase diagrams of the first four scenarios are shown in According to the evolutionary equilibrium results of the eight scenarios, the following proposition can be obtained.Proposition 2.(i) If (ii) If (iii) If Based on the analysis of each scenario above, we can easily get Proposition 2, where (i) corresponds to scenario 1 and 3; (ii) corresponds to scenario 1, 2, 5 and 6; (iii) corresponds to scenario 7 and 8. For (i), when conditions The parameters in the first row of The analysis above mainly focuses on the impact of policy changes of the government sectors on evolutionary result. For the private sectors, the cost difference between different quality services affects the value of Observation 1.When Observation 1 shows that, it is difficult to achieve an ideal evolutionary result when the cost difference between different quality services is too large. Moreover, which evolutionary equilibrium the game eventually evolves to depends on the initial states of the participants and parameter values. We can make the game eventually evolve to  by adjusting the related parameters.In scenario 1, the evolutionary result can be either  or . The probability of the evolutionary result in which direction depends on the area of ABEC and BECD in Proposition 3.In Scenario 1, the probability of the game evolving to  increases when the value of From Proposition 3, we can see that, the higher the unit cost of low-quality services is, the higher the fines of providing low-quality services are, and the higher the unit subsidy for providing elderly care services are, the higher the probability for the system evolving to  is. Moreover, the smaller the unit cost of high-quality services is, the fewer the elderly served by a single private sector is, the smaller the government’s supervision cost is, and the smaller the compensation paid to the customer is, the higher the probability for the system evolving to  is. For the private sectors, providing low-quality elderly care services may lead to fines and the failure to obtain subsidies from the government sectors. Meanwhile, low-quality services will increase the operation risks. Hence, when the costs difference between different quality services is not enough to make up for the loss of low-quality services, the private sectors will choose to provide high-quality services. In addition, the number of elderly people served by a single service provider should not be too large  of The evolutionary paths of two initial strategy states  and  are shown in The fluctuation in the demand for elderly care services will not be too large in the short term. However, in the long run, government policy, changes in demographic structure, regional disparity, or some haphazard events may affect the demand for elderly care services. Let Since the evolutionary result of scenario 3 is ideal from the government’s perspective, we take scenario 3 as an example to explore the impacts of changes in demand on the evolutionary results.When the conditions of scenario 3 are met, the following statements hold: Proposition 4.When considering the out-of-range demand disruption, we have:(i) Equilibrium point  is the ESS when (ii) Equilibrium point  and  are the ESS when (iii) Equilibrium point  is the ESS when There are three main nodal values We consider the scenario where the government sectors change the subsidy policy to a dynamic one. That is, the government sectors provide a high subsidy to the private sectors when the percentage of providing high-quality services is low; otherwise, the government sectors adopt the policy of reducing the subsidy. Assume that the government subsidy is inversely proportional to the proportion of high-quality services. The subsidy then changes from The four fixed equilibriums of the system are The expressions of When Therefore, when the government sectors choose to implement a dynamic subsidy strategy, formulating a reasonable penalty policy for the private sectors providing low-quality services is necessary. The evolutionary stable results of scenarios 1–3 under the dynamic subsidy are as same as the replicator dynamic system in Equations (4) and (5). To understand the impacts of the dynamic subsidy policy on government spending, we have the following observation for Scenarios 1 and 3.Observation 2.When the conditions of scenario 1 are met, if the subsidy of the government sectors meets condition The observation above is obvious if the subsidy under dynamic subsidy policy When point From the above expression, we can obtain Proposition 5.Proposition 5.In scenario 1, by keeping other parameters remain unchanged, the probability of the game evolving to  increases when the value of For scenario 1, the former part of Proposition 5 is similar to Proposition 3 without the dynamic subsidy strategy. The government sectors can take some measures to make the game more likely to evolve towards the ideal result, for example, increasing the maximum subsidy amount, increasing the penalty for private sectors providing low-quality services, or improving work efficiency to reduce the supervision cost. For scenario 4, the values of For a better understanding of the above conclusions, we set a numerical simulation as an example. At first, we present scenario 4 under static subsidy strategy. For scenario 4, the game cannot reach a steady state, since the four evolutionary equilibriums are all saddle points. Further, we observe the evolutionary process of scenario 4 by a numerical simulation. For example, the values of the parameters are: The parameter settings of scenario 4 under dynamic strategy are the same as the static subsidy strategy, moreover, we set From (1)As for the government sectors, when the net revenue of the government sectors implementing supervision is positive, the government sectors choose to implement supervision strategy . Otherwise, the government sectors choose to implement non-supervision strategy  or even cannot reach a stable strategy (scenario 4).In this paper, we mainly focus on the behavioral decision-making process and results of the government sectors and private sectors in the provision process of elderly care services. Parameters like supervision cost, fine and subsidy can influence the government sectors’ supervision strategy, while the private sectors often respond to government policies, service cost and consumer demand. Moreover, each type of participants also interacts with each other in the long-term decision-making process. Therefore, this paper provides insights into how the government sectors and the private sectors make decisions under different scenarios, demand disturbance and dynamic subsidy strategy. The following (1), (2), and (3) summarize the main conclusions and answer the three questions raised in the Introduction section, respectively. Moreover, policy recommendations to promote the private sectors to provide high-quality elderly care services are also listed below.(2)The increase in subsidy for unit service and fine for providing low-quality services or the decrease in supervision cost will increase the probability the private sectors evolving towards providing high-quality services. Moreover, when the cost difference between different quality of services is less than the boundary value described in Observation 1, the increase in the cost of low-quality services or the decrease in the cost of high-quality services will promote the private sectors evolving towards providing high-quality services. .As for the private sectors, when the government sectors adopt non-supervision strategy, the private sectors have no incentive to choose to provide high quality services. When the government sectors choose to implement supervision strategy and the net revenue of providing high-quality services is positive, the private sectors will choose to provide high-quality services.Necessary conditions exist under which the change of service demand will not affect the final decision-making of the system. When the change in service demand meets certain conditions shown in Proposition 4 (i) and (iii), the government sectors choose to implement supervision while the private sectors provide low-quality services. When the change in service demand meets the condition shown in Proposition 4 (ii), the government sectors choose to implement supervision while the private sectors provide high-quality services or the government sectors choose to implement non-supervision while the private sectors provide low-quality services, which depends on the initial decision states of the two types of participants. (Take scenario 3 as an example).(3)For the government sectors, if the evolutionary result is not the ideal one, the government sectors can take measures to promote the game evolving towards the ideal result. For instance, increasing penalties for low-quality services, increasing the subsidies to private service providers, reducing the supervision cost and reducing the compensation to the elder customers. These measures are all conducive to promoting the private sectors to provide high-quality elderly care services.When the government sectors adopt a dynamic subsidy policy, a reasonable penalty policy for the private sectors providing low-quality services is necessary. Additionally, when certain conditions are met (see details in Observation 2), adopting the dynamic subsidy strategy is conducive to saving the government sectors’ expenditure. When the budget, penalty, and the unit cost of providing low-quality services increases or the supervision cost, the compensation to the customers and the unit cost of providing high-quality services decreases, the probability of the system evolving towards  increases. Moreover, the probability of the private sectors chooses to provide high-quality services increases if the penalty (the maximum government subsidy) increases or the supervision cost (compensation) decreases. In addition, the system can reach a stable equilibrium under dynamic subsidy policy, while under static subsidy policy the two types of participants are in an unstable state and cannot achieve a stable equilibrium (scenario 4).To promote the private sectors to provide high-quality elderly care services, we give the following policy recommendations:Firstly, for quality assurance, the government sectors should maintain a supervision state since the private sectors may be speculative. If the government sectors implement non-supervision strategy, the private sectors will not choose to provide high-quality services because of its profit-making nature. The government sectors need to take measures to enhance the supervision efficiency; moreover, research and data collection are needed to support the formulation of related policies.Secondly, the government sectors need to specify the minimum access standards and service standards when formulating policies related to the provision of elderly care services. Moreover, to reduce the possibility of private sectors providing low quality services, the government should increase the punishment of the private sectors for providing low-quality services. Moreover, while supervising private sectors, the government sectors can rate the private sectors and reward those with higher ratings. Integrating the prescribed service standards with the reward and punishment mechanism can ensure the implementation of the policy.Thirdly, increasing subsidies to the private sectors promotes the provision of high-quality elderly care services. The government should increase the policy support to the private sectors. At present, construction subsidies, operating subsidies, general taxation exemptions and land allotment policies have been proposed and implemented. Policies that are more suitable for different regions and different times need to be put forward. Moreover, while strengthening supervision, the government sectors should study the behavior of private sectors. According to the actual situation, dynamic subsidy strategies can be considered when certain conditions are met, which will help the government sectors to save financial subsidy expenditures.At last, facing the limited budget and increasing demand for elderly care services, the government sectors should establish a reasonable financial support framework for elderly care services. Moreover, the policy makers can design reasonable health promotion programs to reduce the related expenditures .An evolutionary game model analyzing the behavioral decision of the government sectors and the private sectors in the provision process of elderly care services is established. Firstly, eight possible evolution scenarios and five possible evolutionary results are given. Then, the necessary conditions to obtain different evolutionary results are summarized and the influence of different factors on the system are analyzed. Secondly, the impact of demand disturbance on the system are analyzed. At last, for a more comprehensive and systematic analysis of the provision process of elderly care service system, we also explore the interaction mechanism between the government sectors and the private sectors under dynamic subsidy policy. Numerical simulations are given to verify our conclusions and make our model analysis easier to understand. The evolutionary model is beneficial to identify the decision-making behaviors of the government sectors and the private sectors. Moreover, the model can not only help the government sectors to formulate relevant policies, but also lead the private sectors in strategy choices under different scenarios and dynamic situation. It can also help the government sectors to establish a feasible long-term care system to meet the growing demand of elderly care services in many countries.There are still some improvements to be made of this paper. Firstly, only two types of participants are considered in the provision process of elderly care services. However, the service receiver (the elderly) can also be considered which will make the model analysis deeper. Moreover, most theoretical articles in the field of operation management contain strong hypotheses, the similar problem in our paper is not inevitable. Further, part of the numerical experimental data derived from empirical estimate. These issues are to be addressed in future research.


Keratoconus is a noninflammatory disease characterized by thinning and bulging of the cornea, generally appearing during adolescence and slowly progressing, causing vision impairment. However, the detection of keratoconus remains difficult in the early stages of the disease because the patient does not feel any pain. Therefore, the development of a method for detecting this disease based on machine and deep learning methods is necessary for early detection in order to provide the appropriate treatment as early as possible to patients. Thus, the objective of this work is to determine the most relevant parameters with respect to the different classifiers used for keratoconus classification based on the keratoconus dataset of Harvard Dataverse. A total of 446 parameters are analyzed out of 3162 observations by 11 different feature selection algorithms. Obtained results showed that sequential forward selection (SFS) method provided a subset of 10 most relevant variables, thus, generating the highest classification performance by the application of random forest (RF) classifier, with an accuracy of 98% and 95% considering 2 and 4 keratoconus classes, respectively. Found classification accuracy applying RF classifier on the selected variables using SFS method achieves the accuracy obtained using all features of the original dataset. In many fields , the resolution of most problems is based on the processing of data extracted from data acquired in the real world and structured in the form of vectors . The quaThere are four important reasons why feature selection is essential. First, spare the model to reduce the number of parameters. Second, to decrease the learning time. Then, to reduce overfilling by improving the generalization and to avoid the problems of dimensionality . So, ourIt is in this context particularly that this work is presented that consists in determining the most relevant parameters for diagnosing keratoconus, which corresponds to a deformation of the cornea (the transparent coating of the iris and the pupil of the eye) which gradually thins , loses iK-nearest neighbors (KNN), decision tree (DT), Naive Bayes (NB), logistic regression (LR), and linear discriminant analysis (LDA) using critical features. Different models will have different strengths in classifying data which will affect classification performance. Also, multiple feature selection methods are used to get the best accuracy. In addition, we mainly review the variable selection application and provide description, analysis, and future research suggestions. The remain of this paper is organized as follows. The following section represents the related works. Keratoconus can be diagnosed during a consultation, motivated by the existence of functional signs secondary to progressive irregular myopic astigmatism. In general, the functional signs are not very specific. The most common is the presence of visual blurring, photophobia, fog, progressive loss of visual acuity predominantly at a distance, monocular diplopia, or persistent irritation . Howeverχ2 and Kruskal-Wallis algorithms. The overall accuracy of this system was 73%. In [Artificial intelligence (AI) has integrated different domains of medicine field such as ophthalmology. The number of works that focused on the detection of ophthalmic diseases using machine learning (ML) is growing. Several research teams aim to build intelligent systems for keratoconus diagnosis and classification. In , authors 73%. In , the autDespite the good performance of different systems already mentioned in the related works, which allowed a very good discrimination between normal and keratoconus eyes in keratoconus classification, many works of them did not mention that they used variable selection method. Such methods could increase system performance, by eliminating irrelevant variables, reducing data dimensionality, and optimizing algorithm prediction time. In this work, we propose a comparative study of keratoconus classification using different classifiers, without and with features selection, by applying different types of variables selection algorithms.The performance of a machine learning system is affected by several factors, including the representation and relevance of the data used by that system. Generally, not all learning data is always relevant to the system. However, the selection of relevant features, by eliminating less informative, redundant, or even irrelevant variables, is of great importance to the learning system. The feature selection model adopted in this work is described in The data preprocessing stage consists generally of eliminating irrelevant and redundant variables, handling missing values in the dataset, and handling categorical data, such as textual data that is difficult to understand for machines. The dataset resulting from this step is then used by different types of algorithms in order to select relevant features.Fast correlation-based filter (FCBF) that allows to select features representing a low correlation with other features and which are more correlated to the target variable using symmetrical uncertainty Mutual information (MI) which can be defined as the measure of reduction of uncertainty of a variable in view of the knowledge of a second variable. It represents a statistical dependence between two random variables, thus, measuring their degree of dependence in the probabilistic sense Analysis of variance (ANOVA) is a statistical model that allows to compare the mathematical expectation of several subsamples in order to demonstrate the possible similarities or differences on specific aspects in a studied sample t defined initiallyVariance algorithm calculates the variance of different features. This algorithm selects the features for which the variance is greater or equal to a special threshold First, the used dataset was filtered using the filters. These methods allow to select variables using different approaches and criteria to calculate the relevance of a variable before the learning phase. In other words, the evaluation of the importance of characteristics is done independently of the use of a classifier. However, the characteristics retained by the filters can be used by all learning algorithms. Filters remove irrelevant, redundant, constant, duplicated, and correlated characteristics in a very efficient manner . The maiRecursive feature elimination (RFE) is a selection feature algorithm in which specific weight values are assigned to features by application of external estimator. This process is repeated recursively, and in each step, attributes whose weights are the smallest ones are removed from the current set. It works until the desired set of features to select from is eventually reached. In the RFE approach, the number of features to select should be initially defined Sequential forward selection (SFS) is an iterative algorithm starting from an empty subset of variables. For each iteration, FFS algorithm evaluates the variables individually and retains the variable that best improves the model. The selection process stops when the performance of the system is no longer increased by adding a new variable Sequential backward selection (SBS) is an iterative algorithm initially using all the features of the dataset. BFE eliminates the least significant variable in each iteration until no performance improvement is noticed Genetic algorithms (GA) are iterative algorithms based on the genetic evolution process. GA constitutes chromosomes from an initial population by proposing potential solutions to the studied problem. This initial population of solution evolves using three operators  to converge to the best solution Hybrid recursive feature addition (HRFA) creates a model using only the most relevant variable selected by ranking different variables of the original dataset. The algorithm adds the most important feature at each step and reassesses the performance of the model . If the The weakness of filters is the fact that they do not consider the learning algorithm when selecting variables. Wrapper methods solve this problem by introducing the learning algorithm during feature selection. This method evaluates the classification performance of a subset of variables during the selection procedure using a classifier . The wraThe feature subset selected by a wrapper method represents a strong dependence on the classifier used in the selection phase. However, changing the classification algorithm can produce poor classification performance.Embedded methods select the features judged critical during the training of the machine learning model adopted for the classification .Hybrid method is a combination of a filter and a wrapper method of features selection. The features retained using the filter algorithm are evaluated by the wrapper algorithm to find the best subset of features .Choosing the right method for selecting features usually depends on the initial goal. Filters are very good in reducing data size and eliminating redundant features. Wrapper methods on the other hand are very powerful at producing good classification precision using a given classifier. The main objective of this work is to compare performance and execution time of different machine learning models in the classification of keratoconus. Classification is realized in first time using all features of the dataset of keratoconus, available in Harvard Dataverse . In the Random forest (RF) is an ensemble of many individual decision trees. It is a classification prediction method which is based on decision trees. This method is proposed by Breiman in 2001 . RF is oIf the data change a little, the performances the individual trees may change but the forest is relatively stable because it is a combination of many trees, and this is the main advantage of RF.Naive Bayes (NB) technique is based on the Bayes theorem. The Naïve Bayes is a probabilistic classifier which is well suited for high dimensional datasets. Despite of its simplicity, NB algorithm can outstrip more efficient other classifiers. NB classifier computes probability estimates rather than predictions. To verify whether a given observation belongs to a specific class, NB algorithm calculates probability each output value. NB assumes that the attributes present do not influence each other and are mutually independent . This isD composed of N attributes, and each tuple of D is structured in N values. Suppose that C1 and C2 are the two available class labels for the target data. For each new tuple X, NB classifier predict that X ∈ Ci if the class Ci has a highest probability condition on X, i.e.,Consider a dataset P(Ci/x) is maximized, this class is called maximum posterior hypothesis. As P(X) is constant for all the classes the equation can be depicted as:If the class Ci had the maximum probability which K-nearest neighbor (KNN) algorithm is a simple and easy supervised machine learning algorithm that can be used to solve classification and regression problems. According to the measure of similarity, like the distance functions, K-NN provides a classification of the new cases, by attributing them to the most present category among these K neighbors [eighbors .The distance of the case to be classified to the other cases is ensured using some norm-based measurement functions, such asK-NN algorithm can be described as follows [The  follows .xj and βj are the features and their corresponding weights/coefficients.Logistic regression (LR) is a statistical-based classification model, and it is a linear predictive algorithm based on the concept of probability. The decision rule of the LR is ensured by a complex function called Sigmoid function. The probability generated by Sigmoid function is limited between 0 and 1. When the predicted value is greater than a threshold, the event is likely to occur, while when this value is below the same threshold, it is not . The SigLinear discriminant analysis (LDA) is a supervised classification technique belonging to competitive machine learning models, developed in 1936 by R. A. Fisher. It is a simple and robust classification method which produces models that provide a good accuracy as more complex methods . The ideThe within-class scatter matrix is calculated using the following mathematical equation :(7)SW=∑c is the total number of distinct classes andwhere x is a sample (a row) and n is the total number of samples within a given class.where The between-class scatter matrix is calculated using the following mathematical equation:The linear discriminants are provided by solving the generalized eigenvalue problem of the following matrix:Decision tree (DT) is a tree-structured classification model. Each node of a DT represents a test evaluating an attribute of any individual in the population. The arcs from a node represent the responses to the test associated with this node. Each sheet of DT corresponds to a class, called the default class. The DT used in this work is based on the CART algorithm presented below .w is a vector of m dimensions and b is a term. The decision function, for an example x, can be expressed as follows:Support vector machine (SVM) consists in finding a hyperplane (straight line in the case of two dimensions) that best separates these two classes in the case of a binary classification . The sepIn reality, most of the problems are multiclass; in this case, solutions based on SVM methods reduce the multiclass problem to a composition of several biclass hyperplanes making it possible to draw the decision boundaries between the different classes.f1-score, ROC curve, and prediction time.In different steps of keratoconus classification, the performance evaluation of obtained results is based in classification accuracy, recall, The precision is a measure that expresses how accurate your model is relatively to those predicted positive, how many of them are actually positive . In our The recall (or true positive rate) is the measure of our model correctly identifying true positives . Thus, ff1-score is a metric combining false positives and false negatives to strike a balance between precision and recall [F1-score is 1, while the model is considered as a total failure when F1-score is 0. F1-score is computed as follows:The d recall . It is aThe accuracy is a popular measure that describes classification performance of the model over all classes . It reprExecution time is the measurement of the time consumed by different machine learning models for the training and prediction phases to perform a classification.Area under ROC curve (AUC) curve is a graph that represents relationship between false positive rate and true positive rate of a test for all possible thresholds. Ordinates represent false positive rate and abscissas correspond to true positive rate. ROC curve expresses the ability of a classifier to differentiate between true positive (TP) and false positive (FP) rates . The valhttps://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/G2CRMO. Structured in csv file, this dataset is composed of 446 features of 3162 rows. Eyes are classified in 4 classes as described in The current comparative study is based on the public keratoconus dataset of Harvard Dataverse , availabThis dataset is extracted and used in  from a dThe different classification models studied were implemented in Python using Jupyter application. All the simulations were carried out with CUDA 10.1 under Ubunto16.04, using a Xeon E5-2697 V4 CPU  ECC: on, a RAM of 64 Gbytes DDR4 2133 MHz, a GPU 1 GTX 1070 Ti , total 38912 threads, ECC: off and a 2 Tesla k80 GPU , total 53,248 threads, ECC: on.Obtained results of first classification task, applying different algorithms of features selection on the original dataset, considering just two classes of eyes  and using different classification models are illustrated in Figures 4Figures 7The same proposed model is evaluated using the original dataset and considering the four classes of eyes as already illustrated in The classification algorithm comparison based on the classification accuracy of different models associated to the classification task considering 4 keratoconus classes is illustrated in Figures The results provided by the previous simulations show that the random forest algorithm represents the highest performance compared to other algorithms, both with and without features selection. RF algorithm allowed keratoconus classification with an accuracy around 98% in the case of classification according to 2 classes and exceeding 91% in the case of the classification considering 4 keratoconus classes. These results are obtained by using a number of variables to be retained fixed at a maximum of 10 for the features selection algorithms which require mentioning the number of features to be selected.The main objective of this work is to present a comparative study of different machine learning models' performances in the case of keratoconus classification, based on the public keratoconus dataset of Harvard Dataverse, both without and with feature selection. Each classification technique was applied using all the variables of the dataset, then by applying 11 features selection algorithms to select relevant variables. To assess studied model's ability to correctly classify keratoconus, 2 classification tasks were performed. The first classification was carried out retaining only 2 classes , and the second classification was carried out considering 4 classes .In overall, RF algorithm has a good ability of differentiating between normal eyes and keratoconus eyes. RF classifier provided the best performance in terms of classification accuracy using all features and for all algorithms of variable selection accepted the filter combined to the HRFA algorithm in the case of 2 and 4 classes of keratoconus. On the other hand, and as illustrated by Generally, algorithms of RF, LR, and LDA represent the best performances in different keratoconus classification tasks. Obtained ROC curves show that RF, LR, and LDA models discriminate accurately different classes of keratoconus using just 10 variables instead of 446 features, hence, the effectiveness of SFS algorithm in the selection of relevant variables, thus, reducing the execution time and material resources of computations. RF algorithm represents the highest performance with an area under curve (AUC) between 98% and 100% across different keratoconus classes. LR and LDA models provide an AUC varying between 94% and 100% for different keratoconus classes.However, concerning the comparison of the feature selection algorithms according to the calculated execution time, this work made it possible to classify these algorithms into 3 categories. A first category of the fastest algorithms which are dedicated to execution on personal computers and whose calculated execution time does not exceed 3 minutes, these algorithms are mutual information, ANOVA, embedded, embedded with filter, filter with RFE, RFE, and finally, filter with HRFA algorithms. The second category of these algorithms concerns algorithms for which the calculated execution time varies from 18 minutes to 313 hours, these algorithms require efficient calculators with good hardware configurations, and this category is composed of filter with SFS, SFS, genetic, and filter with SBS algorithms. The third category is composed of algorithms for which the execution time exceeds 300 hours, and the algorithms of this category are SBS algorithm which was applied just on the case of keratoconus classification considering two classes, due to the expensive prediction time it consumed. In order to validate the proposed methodology, the adopted process is applied on the database keratoconus  composedIn the case of binary classification considering 2 keratoconus classes  and using a subset of six selected variables, the highest performance was achieved, applying 10-fold cross-validation, by RF classifier using genetic selection features algorithm. The best-obtained accuracy was in the range of 93%. In the case of 6 keratoconus classes, the highest performance was provided by the NB model, trained on a subset of 6 selected variables using Boruta  algorithIn conclusion, the current work represented a comparative study of keratoconus classification performances using different machine learning classifiers. The classification was performed in 2 steps, retaining 2 target classes then considering 4 target classes, applying and without features selection. The obtained results demonstrated that RF algorithm combined to SFS algorithm, which has selected just 10 features, provided a classification accuracy relatively higher than the use of all features, i.e., 446 variables. Given the importance of execution time in addition to classification performance, the use of SFS algorithm has reduced significatively the execution time and has increased classification accuracy by eliminating harmful variables to classification models, hence, the usefulness and the impact of including selection of critical and relevant features to be used in the classification, especially in the case of largest datasets. This work was carried out as part of a project involving machine and deep learning, in the field of ophthalmology, which aims to produce an intelligent system capable of detecting and classifying keratoconus based on the analysis of topographic maps of the eyes.