The Swiss Federal Act on Narcotics allows for the restricted medical use of scheduled psychotropic drugs in cases of resistance to standard treatment, and preliminary evidence of efficacy of the scheduled drug for the particular condition. Since 2014, the authors have obtained 50 licenses on a case-by-case basis and developed a psychedelic-assisted group therapy model utilizing MDMA and LSD. The majority of the patients taking part in the psychedelic group therapy suffered from chronic complex post-traumatic stress disorder (c-PTSD), dissociative, and other post-traumatic disorders. Treatment modalities, typical developments and problems encountered during and after the psychedelic experiences are described. Recurrent depression poses a frequent problem, and requires special attention. Symptoms of c-PTSD predominantly addressed by the psychedelic experiences are the regulation of emotions and impulses, negative self-perception, alterations in relationships to others, as well as meaning, recall, and processing of traumatic memories. C-PTSD needs a larger number of psychedelic experiences in contrast to PTSD resulting from single trauma. In this model MDMA was most often used in the first phase to enhance motivation to change, strengthen the therapeutic alliance, allowing it to become more resilient, stress-relieved and less ambivalent. When emotional self-regulation, negative self-perception and structural dissociation had also begun to improve and trauma exposure was better tolerated, LSD was introduced to intensify and deepen the therapeutic process. The majority of participants improved by clinical judgement, and no serious adverse events occurred. A short case vignette describes a typical process. The experiences with this model can serve to further develop the method of psychedelic-assisted psychotherapy (PAP) and to give directions for future research. Since the discovery of LSD by Albert Hofmann in 1943, there have been many attempts to prove the effectiveness of psychedelics such as LSD and psilocybin as adjuncts to psychotherapy. In the 1950's to the 1970's LSD was tested for treating anxiety, depression and pain in advanced stage cancer , the treThe entactogenic compound MDMA met a similar fate. After its introduction into psychotherapy in the late 1970's, when its anxiolytic and prosocial effects were used to treat trauma-related disorders, anxiety disorders and in couples therapy , it rapiAll of the above-mentioned studies used an individual setting with one or two sitters/therapists per patient. The only documented exceptions to the dominant single setting in psychedelic psychotherapy took place in Switzerland from 1988 to 1993, when a small number of psychiatrists in private practice held licenses for the application of MDMA and LSD in psychotherapy also using a group setting .Another more recent exception is a study of psilocybin-assisted group psychotherapy for demoralized male long-term AIDS survivors . This stThe differences in the model we present are:a) Our patients participated within the framework of—on one hand—individual talk therapy and—on the other hand—group sessions in which all patients simultaneously took a psychedelic substance.b) Psilocybin was used in the 2020 study as a one-time adjunct to conventional (group) psychotherapy, where we administered a psychedelic compound multiple times accompanied by integrative psychotherapy.c) The psilocybin study had a rigorous scientific-methodological background examining a well-defined study population in contrast to our purely clinical setting with a mixed population.The purpose of this article is to describe the application of MDMA and LSD as adjuncts and catalysers of psychotherapy in a mixed clinical population of patients who did not respond to standard treatment, using a group model, suggesting the feasibility and safety of this model and highlighting the characteristics and typical developments in the treatment of trauma-related disorders. Because of the regulatory limitations, research is not allowed so as to not circumvent regular drug development practice, and we therefore did not use standard psychometric scales regularly. Our starting point in 2014 was therefore a purely clinical situation without any research ambitions, resulting in only a very coarse, descriptive evaluation of the treatment results.In the United States, and in some other countries, a similar program called “Expanded Access,” applied for by the Multidisciplinary Association for Psychedelic Studies (MAPS), was approved by the FDA in 2019. The program's purpose is much the same as the one for limited medical use in Switzerland, namely to grant access to potentially beneficial investigational treatments for people facing a serious or immediately life-threatening condition for which there is no satisfactory treatment currently available , but requires that existing treatments are ineffective and that preliminary scientific evidence suggests the efficacy of a scheduled drug for the particular conditionAfter the Swiss MDMA/PTSD study and the Swiss LSD/anxiety in life-threatening disease study results were published in 2013 and 2014 , 15 the In a first phase beginning in 2014, MDMA or LSD was administered in an individual setting. From 2015, a psychedelic-assisted group therapy model was established. Over the course of time, patients predominantly with trauma-related disorders, especially complex post-traumatic stress disorder (c-PTSD) were admitted to the group. All patients had previously undergone multiple psychotherapeutic and psychopharmacological treatments and had failed to improve in regard to symptom reduction and general wellbeing and were therefore considered treatment-resistant.A more detailed article on the history and nature of psychedelic-assisted group therapy was recently published by Gasser .The collaboration between the authors ended in 2020 and the group was closed.Due to the growing publicity regarding MDMA for PTSD, the focus of referrals and requests for therapy in the first author's practice shifted increasingly toward trauma-associated disorders. This led to a predominance of trauma-associated diagnoses in the presently described patient population. Furthermore, when we initiated the group, patients from the first author's practice were in the majority. These circumstances certainly influenced the general atmosphere and content-related orientation of the group, but a specific “tailoring” of the overall therapeutic approach was not necessary or intended. Also, we did not in any way limit the access to the group by favoring trauma-related disorders. As for the cluster headache/migraine subgroup , all thoWe treated a total of 50 patients between 2015 and 2020. Treatment-resistance in the case of trauma-related disorders was defined as having had at least two unsuccessful courses of psychotherapy and at least one psychopharmacolo-gical treatment with an SSRI or SNRI. In the case of depression and anxiety disorders, treatment-resistance was defined as not having sufficiently responded to at least 2 antidepressants, augmentation strategy and psychotherapy.All patients participating in psychedelic-assisted psychotherapy were required to be in regular psychotherapy with one of the authors. In exceptional circumstances, we treated patients with psychedelic-assisted psychotherapy who were under treatment of an external or referring therapist. In this case, patients were required to have a series of diagnostic and introductory sessions and at least one integrative psychotherapy session after each psychedelic-assisted experience with one of us. They were also required to agree to a professional exchange between all therapists involved in the treatment.Borderline personality disorder (BPD) as an index diagnosis was excluded. A history of psychotic episodes or bipolar disorder in patients and in first-degree relatives were considered as a contraindication and therefore motives for exclusion. Four cases with an index diagnosis of c-PTSD had comorbid borderline personality traits. These patients were carefully assessed in regard to the risk of self-harm, suicidality, impulsivity and the stability of the therapeutic relationship before being accepted for psychedelic-assisted psychotherapy. Patients with acute drug dependency were excluded. Cannabis consumption for medical reasons was accepted.During the reporting period, we rejected a very large number of requests and referrals due to the above-mentioned exclusion criteria such as bipolar disorder, psychosis (borderline) personality disorder, but mainly due to limited capacities, requests from outside Switzerland, no prior standard treatments and young age (<20 y).The MDMA and LSD were provided by the Pharmacological Department of the University Hospital of Basel, Switzerland, which was responsible for all handling, quality controlling and encapsulation. MDMA  was administered in 100 and 25 mg capsules. LSD (Lysergic acid diethylamide-HCl) was supplied in drinking vials  100 and 25 mcg. Until 2020 only LSD and MDMA were available, but since then psilocybin has also become an option.Psychotropic medications with the potential to interact with or which could dampen the effects of MDMA or LSD (antidepressants and neuroleptics) were discontinued at least five half-lives before the psychedelic-assisted sessions. The duration of tapering was 1–2 weeks, depending on the original dose level and the individual tolerance of rapid dose reduction.All somatic medications such as antihypertensive drugs, thyroid preparations or anti-Parkinson's medication were continued.MDMA was indicated primarily for the first phase of psychedelic-assisted psychotherapy because of its effects, which are therapeutically and subjectively easier to handle and not so overwhelming (in contrast to LSD), its anxiolytic and prosocial properties, as well as to enhance motivation to change, to strengthen the therapeutic alliance to become more resilient, stress-relieved and less ambivalent. Patients with severe trauma-related disorders particularly benefit from a gradual approach beginning with lower doses of MDMA (75–100 mg), which facilitates the building of trust and feeling of security and strengthening the resilience of the therapeutic alliance. The maximum dose of MDMA was 125 mg. In some rare cases, a booster dose of 50 mg was given after ~2 h in situations where the effects of MDMA were weak or very short.LSD was indicated for later stages of the therapy when some trauma processing had already taken place and exposure to traumatic material could better be tolerated. In particular, negative self-beliefs deeply anchored in the personality responded only to LSD. Switching from MDMA to LSD was based on clinical judgement as well as the readiness of the patient and his or her trust in the therapeutic process to go deeper and allow for more confrontation.If trauma was not the main focus, such as in OCD, depression or with end-of-life issues, LSD was administered from the outset. The dose of LSD ranged from 100 to 200 mcg, depending on the target symptoms, personality and psychological defense structures. Patients who were rigid, emotionally highly controlled and compulsive needed higher doses, whereas emotional instability, impulsiveness, and histrionic personality structure would benefit more from lower doses. In most cases, the optimal dosage of LSD was titrated over the first few sessions. In general, this dose range was found to be optimal for producing the desired drug effects while at same time allowing for participation in the group process.Our model is based on and further developed from one which was already used in Switzerland from 1988 to 93 . Our praIn order to fully understand the effects of this therapy, the four perspectives of set, setting, substance and sitter/therapist have to be taken into account. In our view, psychedelic therapists should have experienced drug-induced altered states of consciousness in a therapeutic setting themselves in order to fully appreciate and understand the mechanisms of action, possibilities, limitations, and pitfalls of the process.Herman first proposed the concept of complex post-traumatic stress disorder (c-PTSD) in 1992. It describes in a coherent and integrative way the multifaceted symptoms of traumatized patients who suffered repeated or prolonged physical, sexual and/or emotional abuse and neglect during childhood and adolescence, often by close caregivers, where escape was not possible due to physical, developmental or environmental/social constraints . The verDespite the clinical usefulness of this concept for diagnosis, understanding and for formulating treatment guidelines, the concept of c-PTSD was for a long time discussed very controversially and was accordingly not included in the DSM-5 revision. In contrast, in the now implemented ICD-11, PTSD, and c-PTSD have been included as two distinct conditions under a general category “Disorders specifically associated with stress” based on preliminary evidence that c-PTSD is a common, more frequent and more debilitating condition than PTSD .We followed the ISTSS guidelines for the treatment of c-PTSD that were valid at the time , 29, whiThe recommended model for treatment for c-PTSD , 29 at tThe common key components of the major existing and empirically supported, effective trauma-focused psychotherapies are: (a) Psychoeducation on the nature and course of psycho-physiological reactions to trauma, how to cope with intrusive memories and management of distress. (b) Emotion regulation and coping skills. (c) Exposure to traumatic memories. (d) Cognitive processing and restructuring and/or meaning making. (e) Targeting emotions such as fear, guilt, shame, anger, or grief and sadness. (f) Reorganization of memory functions and creation of a coherent trauma narrative .Reasons for first starting with individual sessions were a strong fear of the psychedelic experience itself or also pronounced fear of the group situation of having to express oneself in front of strangers. A further frequent objection to the group was observed in the presence of a severe shame issues, as is quite common in cases of sexual trauma. Even when participants regularly attended the group it could happen that in extraordinary therapeutic situations individual psychedelic-assisted sessions were added. The intervals between psychedelic-assisted sessions varied substantially, depending on the therapeutic process and the pace of integration as well as other factors such as professional obligations that could not be postponed. Only a small number of patients attended all available group sessions.Before a patient engaged in trauma-focused psychedelic-assisted psychotherapy, the following steps were necessary:a) Psychoeducation: Conveying a comprehensive map of consciousness, how humans react acutely and chronically to trauma, the nature of psychedelic-assisted psychotherapy, risks and benefits and what patients can expect from the therapist and from psychedelics-assisted psychotherapy.b) Establishing a therapeutic relationship and alliance, which from the perspective of the therapist is stable enough to be able to support the patient during and after the anticipated phases of emotionally charged confrontation with traumatic material occasioned by the psychedelic experience.c) Learning basic skills for awareness and regulation of emotions, e.g., self-soothing and breathing techniques, as well as for ensuring personal safety.d) Formulating a tentative working hypothesis on how symptoms developed and are related to the biography and the trauma history.The psychedelic-assisted group sessions took place four times a year  in the group room of the private practice of the first author located in a quiet residential area on the outskirts of a small town in Switzerland. The dates of the sessions were scheduled in advance and were communicated to the participants. Two separate rooms were available in case someone felt too exposed while in the group, urgently needed to talk with one of the therapists, or felt overstimulated and wanted to retreat for a while. The location offered the possibility to go outside and experience nature if desired. The number of participants was limited to twelve, with three therapists of which one was female. A larger group would have overstrained the resources of the therapists to appropriately guide the group and support participants in their individual process and also unduly limit time for individual preparation before the session as well as during the sharing after the psychedelic experience.Because the MDMA experience is of shorter duration than with LSD and because some participants would become talkative, restless or wished to interact with others under the influence of MDMA, there was a need to structure and guide the group experience so that participants experiencing LSD were not disturbed or distracted too much. During the first 4–5 h of the experience we therefore advised the participants to refrain from direct interactions with other group members in order to not disturb the unfolding and deepening of the inner process, i.e., mystical-type peak experience in the opening and plateau phases of the experience.From one session to the next, the two authors consistently alternated in the role of main guide. The main guide was responsible for the decoration of the room , the moderation of group discussions, the selection and playing of music, as well as for giving general instructions and guiding the group during the substance experience. The two other therapists acted as co-therapists/sitters, supporting anyone who required or requested help or attention.A 3-day format was used for the LSD or MDMA experience. Participants met in the evening before the psychedelic experience for 3 h beginning with warm-up exercises such as breath or body awareness exercises. This was followed by the presentation of new group members and the discussion of recent developments, problems, expectations, concerns and fears of the participants as well as setting of intentions for the next day. Participants were encouraged to interact with each other in the discussion. The therapists finally answered questions about dosage, effects and procedures of the LSD/MDMA experience and also gave instructions on how to appropriately manage the altered state of consciousness and cope with difficulties such as anxiety or distressing physical/emotional states and/or memories. The participants then decided where in the room and beside whom they wanted to spend the following day and accordingly arranged their places.Participants reclined on mattresses in a circle, and armchairs were available if, for example, participants were aged, disabled, or had trouble getting up from the floor. Some patients brought various meaningful personal belongings, souvenirs or photographs, which were arranged in the middle of the circle. The evening closed with a piece of music. Participants spent the night in the group room, at home or at a local B&B or hotel if they came from out of town.On the day of the psychedelic experience, the group would meet at 9.30 a.m. Last minute questions and concerns were addressed and/or short contributions were made, e.g., sharing a dream. The ingestion of the substances took place at about 10 a.m. To shorten the time until the onset of effects and to reduce anxiety  the main guide repeated instructions or suggested some body awareness exercises.Participants were advised to keep their eyes closed as much as possible and to direct attention to their inner process. We did not use blindfolds, but these were available on request. It was therefore up to the participants to learn to guide and focus attention, similarly to many meditation traditions. Music and silence/stillness alternated.Music is an invaluable and essential ingredient of most forms of psychedelic-assisted psychotherapy, and holds the potential to touch and influence the psyche beyond the conscious and verbal-cognitive dimension –33. We aThe music we played was carefully selected according to the phase of the experience, the atmosphere of the moment in the group, the flavor, rhythm and message of the music and lyrics as well as its intended effects . We played music which to the participants was new and unknown, carefully monitoring its immediate effects on the group and the individuals. Stillness is considered a tool of confrontation and is at the same time a typical (blissful) feature of the mystical-type peak experience .The therapists monitored, moved around the room, and sat with participants spontaneously and on request. We checked on their process but avoided lengthy verbal exchanges. If there were no issues, we sat quietly with them. If a problem arose, participants were verbally instructed on how to manage the difficult situation, offering touch (holding hands or putting a hand on a tense or painful spot of the body), thus helping the patient to overcome avoidance and resistance, and redirecting their awareness to the therapeutic process.Vital signs  were monitored only in exceptional circumstances, when necessary, or when the clinical situation was unclear .About 6–7 h after ingestion of the substance and depending on the extent to which its effects had worn off, we invited the participants to express how they were feeling and to give short statements concerning what they had experienced so far. This frequently helped participants who were stuck or distressed and confused about their experience to relax, re-orient and start to cognitively reflect and integrate the experience.At about 6 p.m. we served a light dinner in the form of a picnic, sitting together on the floor of the group room. At 7 p.m. we closed the group session and participants could then stay together for the rest of the evening without the therapists, talk together or listen to music, go for a walk or go home. We then drove people to wherever they were staying for the night.On the final day, the group met again at 9.30 a.m. We began by listening to a piece of music played the previous day, in order to help participants tune in to their experience again. All participants were then invited to share their experience in detail. This integrative talking session was considered of utmost importance, aimed at helping the participants verbalize the rich, blissful, ineffable and yet often overwhelming, difficult and painful experience, which reflected their psychodynamic and spiritual process.Verbalizing is an important and crucial step toward understanding and integration. It is also an invaluable opportunity for verbal therapeutic interventions as the participants were still in a very open, non-defensive and responsive mental and emotional state. The aspect of group dynamics on the day after was also more prominent and visible. Experiencing feedback and compassion from other group members further facilitated and potentiated the individual integration process. The integration talking session took about 4 h and terminated with final instructions for the following time on what do in case of an emotional crisis, sudden unexpected recall of additional traumatic material, confusing thoughts, etc. We once again ended by listening to some music together and then tidying up the room.All participants were required to write a comprehensive report of the experience and fill out the 5D-ASC (5 Dimensions Altered States of Consciousness) and the MEQ  questionnaires. The reports were discussed in the regular integrative psychotherapy. Reports and questionnaires were subject to an accompanying study approved by the FOPH examining reported acute drug effects .Participants received a take-home CD or a list of the tracks that were played. Listening to the music later helped to resolve momentary difficult emotional situations and was helpful in the further integration process.From 2014 to 2020, 22 group sessions took place. Initially, patients with trauma-related disorders, as well as OCD, depression, cluster headache, anxiety disorders in conjunction with Parkinson's disease and multiple sclerosis were included in the group. We quickly realized that for the forging of a stable working alliance within the group, the individual goals diverged too much. Participants with trauma-related disorders, anxiety disorders and depression, already primed by previous psychotherapies, implicitly accepted that this therapy required a lengthier individual and group therapeutic process which involved questioning themselves, revisiting traumatic events and engaging in a process with the group, whereas participants with other diagnoses, e.g., with cluster headache, had more short-term goals such as quick symptom reduction. Moreover, cluster-headache treatment with psychedelics is considered as more of a pharmacological than a psychotherapeutic treatment.Over time a core group of participants who continuously attended psychedelic-assisted sessions was formed. They also began to meet and provide mutual support outside of the therapy, and new friendships developed. The more advanced they were in their individual long-term therapeutic process the more they engaged directly in supporting and confronting their peers during the sessions in a co-therapeutic sense, as well as taking care of and serving as a model for newcomers, helping to experience what secure attachment, mutual responsibility and care for each other really mean.As in every group, conflicts later arose, for example, from transference. We usually advised that the conflict in the group be declared before the experience, in order to focus on one's own part of the conflict and to try to resolve the conflict with the person involved during the last phase of the experience or during the sharing on the 3rd day, when participants are more open, compassionate and less defensive.Another observation was that specific issues would manifest and spread across the group, such as a specific emotion like fear or a focus on relationships to important figures of childhood, which would then be utilized therapeutically. More experienced participants were generally more conscious of and open to the group process, and would express their perceptions spontaneously, by saying for example “I perceive so much anger in the group…” Preconscious conflicts and ineffable childhood dramas tended to be re-enacted in the group. These kinds of group dynamics are not specific to psychedelic-assisted groups, but can be enhanced considerably under the influence of psychedelics.The fact that Peter Gasser treated more patients with LSD is simply due on one hand to the fact that his patient pool contained more cases with anxiety disorders and cluster headache/migraine cases, for which psychedelic treatment was initiated directly with LSD, and on the other hand that he was more familiar and comfortable with LSD. Peter Oehen's patient pool, on the contrary, contained more trauma-associated cases, with MDMA being the primary indication based on current data.The most frequent diagnosis being c-PTSD, we were able to distinguish a typical pattern of the therapeutic process in this subpopulation. Despite optimal preparation, the first psychedelic-assisted sessions were usually very trying for all involved. In the initial MDMA experiences most patients experienced first a short phase with positive and pleasant MDMA effects followed by a confrontational phase with direct recall of traumatic material and intense negative emotions. In cases of dissociative amnesia for the trauma, the recollection of the trauma often began with somatic symptoms such as pain, cramps, paraesthesia, etc., often located in the traumatized areas of the body, then moving on to sensory perceptions e.g., sounds, smells, and/or fragmentary images and memories.A complete process of recollection of trauma could range from one to a lengthy series of psychedelic-assisted sessions depending on how early in life the traumatization took place and how extensive it was. In cases of severe dissociative states or non-epileptic seizures, these tended to be activated first and then needed special attention to help patients reorient and to gradually tolerate the underlying emotional distress. It was only then that the recollection and reprocessing of trauma would begin.In parallel or with some delay, the dysfunctional relationship patterns and attachment problems emerged and became a second crucial focus of therapy.Another observation concerned the fact that after a certain number of sessions, patients kept reliving similar traumatic events without gaining any further benefit from this confrontation (“looping”). At this point, they were guided to shift attention away from these memories and to focus more on the here and now of their lives, i.e., on resolving the trauma sequelae. This was also a reason for switching from MDMA to LSD. In general, we made the observation that the occurrence of the typical positive mystical type experience (MTE) led to more favorable post-session developments. In patients with more pronounced treatment needs such MTE were only observed in later phases of therapy. Even without the occurrence of MTE, these patients made substantial progress.In the case of trauma-related disorders, the major symptom clusters were assessed to determine the outcome (see paragraph “complex post-traumatic disorder”). All five symptom clusters of C-PTSD were attenuated. The clearest improvements were enhanced emotion regulation and relational capacities, as well as a decrease of intrusive and dissociative symptoms. Continued improvement was observed with each session. Overall, of the 21 patients with trauma-related disorders, four achieved remission, 13 had improved and three did not improve. Two of ten cases with anxiety disorders remitted, five cases improved clinically, and three cases did not improve. The OCD subgroup showed one case with remission and one non-improved case. The cluster headache subgroup contained only on case of improvement in contrast to three cases with no improvement and unfortunately one case with a deteroration (see below). In the ASD subgroup one individual improved and the other did not improve.At the end of the reporting period, 20 of 50 participants were still in ongoing (partly psychedelic-assisted) psychotherapy, with further reductions of symptoms and improvement of wellbeing.Pre-existing antidepressant medication was a problem for which there was not yet a good or consistent solution available. On one hand, short-term tapering as we used in our method, has been shown to diminish response to MDMA-assisted therapy . On the In two cases, the dose of the antidepressant medication was lowered but not stopped  because of these difficulties. Both patients reported having experienced “a strange trip,” meaning that they felt uncomfortably emotionally numb or detached during their psychedelic experience. Furthermore, no obvious relationship between prior antidepressant medication and improvement was noticed.Patients with a depressive disorder (10 cases) or with a comorbid chronic/recurrent depression to c-PTSD (in 12 cases) who were under treatment with antidepressants until the psychedelic experience and who then discontinued medications tended to relapse after MDMA although the therapy and trauma processing progressed. Especially in the beginning of a relapse of depression following a substance experience it was hard to discern “normal” but emotionally difficult and trying trauma processing from symptoms associated with depression. This pattern was observed more after MDMA and much less after LSD. We therefore resorted to reinstalling the antidepressant medication immediately after sessions, or as soon as a relapse of depression was suspected. The relapse of depression usually took place in a time span of 3–6 weeks. After two or three such episodes, individual cues could be identified which allowed for the timely reinstallation of antidepressant medication.We observed that comorbid depression to trauma-related disorders tended to improve (four out of twelve) or remit completely (eight out of twelve) in later phases of therapy. Antidepressants could be stopped in five cases and had to be continued in two cases .In depression as index diagnosis, two of 10 cases achieved remission, four of 10 cases improved clinically, and four of 10 cases did not improve at all.One 48-year-old woman showed a prolonged delusional phase after LSD in the context of an especially painful and confusing episode of childhood sexual abuse, which resolved during the integrative psychotherapy, requiring a limited medication with quetiapine 25–50 mg for sleep.Another 38-year old woman suffering severely from cluster headache for more than 10 years attended one group session with LSD 100 mcg. She had used high doses of all kinds of analgesics, tryptanes, and ketamine nasal spray for acute headache attacks. During this session, she developed an acute severe headache attack that was successfully treated with ketamine and lorazepam. She felt disappointed and refused to repeat the LSD experience.During the period of acute drug effects during the session, nobody tried to leave the premises. Some patients requested to sit outside on the balcony of the group room for a certain time or wanted to be alone in the annex room. We had several confrontations with heavy smokers who wanted to go outdoors to smoke during the psychedelic experience, which had not been part of the agreement or group rules. It usually turned out that the urge to smoke was related to something unpleasant happening inside which they wanted to avoid by smoking. Leaving the group room all too frequently for snacks or restroom visits were similar avoidance patterns we observed. Another avoidance pattern that needed to be addressed was when patients sat up, started walking around, started obsessively taking notes, etc. Chattering, which distracted fellow participants was a minor but frequent problem that also needed to be addressed.Patients with comorbid borderline traits tended to have more difficult psychedelic experiences that were emotionally more intense, overwhelming and distressing. These required more support from the therapists. Interestingly, they also received a lot of understanding, compassion and often “co-therapeutic support”  from fellow patients. Until the emotional regulation capacity improved, the integration phase in the weeks afterwards was often similarly turbulent and erratic, requiring close follow-up. Suicidal thoughts and mild self-harm were reported several times, but no suicide attempts happened. It was possible to manage these situations within the usual framework of integrative psychotherapy.Unforeseen early termination of treatment happened in two cases where patients did not comply with the agreements of the treatment and did not engage appropriately in the integrative psychotherapy. Another reason was in one case a first difficult psychedelic experience and consecutive reluctance to continue this form of treatment. One patient discontinued the treatment unexpectedly following a (transference) conflict with one of the therapists, which could not be addressed adequately.The most common conflicts between group participants involved disruptive behavior  during the experience or when someone was overly indirect during the sharing on the 3rd day, avoiding talking in a personal and authentic manner about their experience.In 2013, following previous depressive episodes, 51-year-old Anne came in for treatment for severe major depression with suicidality. She had followed continuous treatment with antidepressants for many years. She worked in the health profession, was married and had two adolescent children. At the age of 16 she had begun to feel unhappy, emotionally numb and repeatedly fell into dissociative states. At 20 years she began the first of three extensive courses of psychotherapy. In summary, the psychotherapies stabilized her in everyday life, reconnected her to her emotions and improved body awareness. However, her traumatic childhood remained unaddressed because of marked avoidance.Unwanted at birth, Anne grew up as the first of three children in a very frosty family atmosphere. Her mother denied her children all physical and emotional contact, was chronically depressed and ailing, and had put the blame solely on Anne for the latter. The only nurturing physical contact she experienced was with her sister with whom she shared a bedroom. The two sisters consoled each other by cuddling and singing together in bed at night. Her father was a sadistic, hot-tempered, violent and unpredictable man who enjoyed inflicting pain and fear upon his children. Anne remembered him almost drowning her several times during swimming lessons and molesting her in the bathroom. She also remembered her father sneaking into their bedroom at night and abusing her sister sexually, leaving her completely helpless and increasing her feelings of guilt for being unable to prevent the abuse. Even today Anne still feels responsible for her sister who consequently developed a severe and disabling BPD and eating disorder in her adolescence. The repetitive witnessing of her sister being sexually abused together with the prolonged physical and emotional neglect and the massive guilt conflict led to deeply rooted emotional and relational problems, negative self-perception and low self-esteem which had troubled her since adolescence. She was chronically distrustful, shunned conflicts when personally involved, was not aware of her personal boundaries and let others take advantage of her out of chronic feelings of guilt and shame. Above all, she was unable to regulate her emotions and impulses appropriately, hurting herself when she was emotionally overwhelmed.She was subsequently diagnosed with chronic depression, including a current severe episode as well as moderate degree complex PTSD. Her depression wore off only slowly under pharmacological treatment with venlafaxine 150 mg/daily. At the same time, she had great difficulties speaking in therapy about her family of origin, repetitively dissociating or going numb when addressing traumatic memories. In this phase we were able to outline her relational and emotional problems, her chronic intrusive and dissociative symptoms and enhance her awareness of the constant distress and avoidance patterns that she had been experiencing for decades, as well as developing a map of the traumatic events and conditions in her childhood.At this point and after being in intensive psychotherapy for more than 1 year she had her first MDMA experience in a group setting. She labeled it an “emotional breakthrough” and apart from experiencing positive and negative emotions of previously unknown intensity, she felt great relief about at last being able to be certain that the abuse of her sister had really happened and acknowledging that it was not her fault that her father had abused her sister. She was now able to speak freely about the abuse despite her father's lifelong tabooing and threats. Depression did relapse after the first MDMA experiences but no longer required medication. The therapeutic alliance was instantly freed of distrust and reluctance. Consequently, nightmares of her father coming into the bedroom at night frightened her increasingly and gradually the suspicion of having been abused herself dawned on her. This was painfully confirmed by the following MDMA experiences. It took eight MDMA sessions to complete the narrative of her own abuse. At the same time, she opened up emotionally in relationships, gaining trust and self-esteem.In the group, she befriended a fellow patient and developed a sister-transference to her. The processing of this transference reaction was very important to overcome her chronic feelings of guilt toward her biological sister and to gain independence, self-worth and authenticity. This led to her being able to interact with her fellow patient (and the others) in a good and increasingly mature way, with clear boundaries.In contrast, she chronically needed reassurance and confirmation of her perceptions and behavior in a childlike manner for a long time during the integrative therapy. Minimal uncertainties and misunderstandings would destabilize and depress her again and again. She also began to worry about what went wrong in early infancy and in the relationship to her mother. For this reason and because the therapy stalled at this point, we switched from MDMA to LSD (in a dose of 150 mcg). In the following four LSD experiences different aspects of the sexual abuse already covered in the MDMA experiences were reviewed and revisited in a much more confrontative, detailed and relentless manner. More importantly, she was able to identify and explore lifelong attachment problems, which turned out to have originated perinatally. Intense feelings of pain, despair, disgust, shame, guilt, abandonment and insecurity burdened her again. Then, after an impressive and overwhelming death-rebirth experience under LSD she was able to change the abovementioned patterns in a short time, abandon her habitual negative self-perception and become increasingly self-confident, assertive, more independent, self-determined and resilient. Earlier, after the first few MDMA experiences, she had already come to terms with her father who suffered from dementia and was able to forgive him. After experiencing LSD, her relationship to her mother improved to the point where her mother admitted her mistakes and failures, making reconciliation possible and enabling closeness to her mother for the first time. Needless to say, the relationship to her husband and children—a secondary focus of the therapy—matured and deepened during this phase. This most recent development allowed for the thinning out of the integrative psychotherapy and the initiation of termination phase of the psychedelic-assisted psychotherapy.At termination of the treatment, she made the following statement when asked about the significance of the group setting for her treatment:I was a very lonely and disconnected person before I joined the group. The psychedelic group experience helped me to open up, to be close to others, to express myself, to become authentic and to build relationships. I realized that other people also had severe problems and to listen to them and watch them change from one session to the next was fascinating, enlightening and encouraging. To talk to the group about all the bad and painful things that had happened to me as a child was an extremely helpful and healing experience. I appreciated the group rules and the clear structure of the workshops. The preparation evening before and the sharing and integration the morning after the experience were very important parts of the treatment.”“The course of Anne's psychedelic-assisted psychotherapy includes all typical aspects of effective trauma-focused therapy: an extensive psychoeducational preparation phase, followed by a lengthy and intense drug-initiated phase of recall and processing leading to a coherent trauma narrative, simultaneously targeting difficult trauma-related emotions and enhancing emotional regulation skills, as well as initiating cognitive restructuring, changes in self-perception and meaning. Parallel to these central focuses, relational problems with significant others were addressed and resolved.One important difference to non-drug-assisted trauma-focused psychotherapy is that the therapeutic relationship became acutely less ambivalent, more stress-relieved, closer and resilient once MDMA was involved. MDMA also increased the change motivation, perseverance and the emotional window of tolerance, as well as decreasing the degree of post-traumatic avoidance substantially. In Anne's case, MDMA alone was not able to address and resolve the early life traumatization together with the corresponding dysfunctional patterns of behavior and self-perception resulting from the maternal rejection, neglect and induction of guilt. MDMA paved the way with the processing of childhood trauma, while LSD addressed the deeply rooted relational, attachment and self-relational problems.Based on modern psychodynamic and psychotraumatological concepts, as well as on the preliminary empirical evidence for psychedelic-assisted psychotherapy, a model of group psychedelic-assisted psychotherapy for a population of patients with a variety of diagnoses is presented, highlighting the treatment of treatment-refractory post-traumatic disorders in which MDMA and LSD were used sequentially. Doses and intervals were adapted to the individual needs and the therapeutic process.The treatment of c-PTSD required larger numbers of psychedelic experiences than the MDMA-assisted treatment of single trauma that is currently being investigated in phase 3 studies . We saw The clinical results for the subgroup of participants with trauma-related disorders were more favorable than in the other subgroups .We also had the impression that a part of the problem of non-improvement or relapse of depression could be due to a more difficult transfer of the insights and psychedelic experiences into everyday life than seen in other disorders such as anxiety disorders.Administering LSD and MDMA in the same group required careful dosing of the substances, as well as consistent structuring and guiding of the group process. We observed the group setting to be more challenging and confrontative than the individual setting by expanding the psychedelic experience with a collective dimension. In our experience, group psychedelic experiences intensified and deepened the individual therapeutic process and made it therapeutically more efficient in regard to outcomes than in an individual setting. The group setting also allowed us to treat more patients in the given time.There were no safety problems and no serious adverse events requiring hospitalization.The psychedelic group therapy model presented here suggests the feasibility and safety of this approach. Given the current high need for more effective treatments for chronic trauma-related disorders, OCD, chronic depression and anxiety disorders, the “restricted medical use program” is an invaluable way to help otherwise treatment-resistant patients until these psychedelics have become registered drugs.Several limitations exist: the outcomes presented here are purely descriptive and based solely on clinical judgement without using standard scales to document improvements, and therefore of very limited significance. Because of the nature and the legal constraints of the “restricted medical use program,” we were not able to establish a prospective and controlled research design.Despite this, the practical experiences that were made with this program can possibly provide directions for future research, the training of future psychedelic therapists and the practical application of these substances once they have been registered as prescription drugs.The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. The patients/participants provided their written informed consent to participate in this study. Written informed consent was obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.PO wrote the first draft of the manuscript. Both authors contributed to the article and approved the submitted version.Open access publication was paid by the Swiss Medical Society for Psycholytic Therapy (SAePT).Both authors work in private psychiatric practices in Switzerland. PG is president of the Swiss Medical Society for Psycholytic Therapy and has counseling agreements with CompassPathways, MindMed, and Reconnect labs.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.


Public health crises have become one of the greatest threats to sustainable global economic development. It is therefore important to explore the impact of public health events on green economic efficiency. However, few studies have specifically examined the relationship between public health security and green economic efficiency. Based on the relevant data of 30 Chinese provinces from 2011 to 2019, this paper explores the impact of public health on green economic efficiency by establishing a four-stage SBM-DEA model to construct green economic efficiency indicators and using a panel model. A moderating effect model is established to explore the moderating effect of environmental regulation on the impact of public health on green economic efficiency. In addition, this paper examines the heterogeneity of public health impact on green economic efficiency in terms of geographic location, carbon pilot, and transportation level. It is found that, first, public health events have a significant hindering effect on green economic efficiency. Second, environmental regulation has a significant moderating effect on the impact of public health events on green economic efficiency. Third, the impact of public health events on green economic efficiency changes from hindering to facilitating as the intensity of environmental regulation increases. Fourth, the impact of public health events on green economic efficiency is heterogeneous in terms of geographic location, carbon pilot, and transportation level. The above studies have implications for how to balance economic development and environmental protection in case of a public safety event. Public health events are characterized by sudden outbreaks, great devastation, rapid spread, and a high degree of uncontrollability . WhetherThe literature studies a large number of factors that affect the efficiency of the green economy, such as technological progress, industrial structure, energy price system, and energy consumption –15. HoweThe contributions of this paper are as follows: First, previous research lacks the use of the four-stage SBM-DEA model to construct green economic efficiency indicators. In this paper, the investigation of green economic efficiency is more systematic and in-depth, and the definition, measurement, and theoretical research system of green economic efficiency are enriched and improved. Second, it is necessary to discuss the impact of public health events on the efficiency of the green economy from the perspective of environmental regulation. It is here confirmed that the negative impact of public security incidents on green economic efficiency can be mitigated by implementing corresponding environmental regulation policies. Third, it is also necessary to discuss the impact of public security incidents on the efficiency of the green economy from the perspectives of regions, traffic levels, and carbon pilots. This will help the local government to adapt to local conditions and take more efficient measures to promote the efficiency of the green economy. In-depth research on the above issues will help clarify the specific mechanism of the impact of public security incidents on the efficiency of the green economy. Fourth, we perform robustness testing and endogeneity testing by replacing models and explained variables, ensuring that research conclusions are more reliable. Fifth, this paper enriches the theory of sustainable development and improves the targeting of policies to provide a theoretical basis for policymakers to formulate sustainable development strategies and to facilitate sustainable economic development.The paper is organized as follows: Section Literature review and mechanistic analysis describes the literature and provides details of the mechanistic analysis. Section Variable selection, model construction, and data sources explains data sources, variable definitions, and empirical models. Section Empirical analysis and discussion includes the benchmark empirical results and their analysis. Section Heterogeneity analysis provides details of the heterogeneity test. Section Robustness testing and endogeneity treatment does so for the robustness test. Section Conclusions and insights sets out the conclusions and insights of the research.The green economy advocates harmony with nature and establishes a positive link between resources, environment, and economic development to create prerequisites and conditions for sustainable economic development . Green ePublic health events have a significant impact on the tourism industry . The traPublic health crises can hit the quality and quantity of the workforce by infection, premature death, and restriction of work activities . A good The occurrence of a public health crisis event often affects investor sentiment, and investors tend to be pessimistic in the short term. If a public health event is never dealt with effectively or even accelerates its spread, it can further exacerbate investors' pessimistic expectations and affect the country's economic confidence . This caIn the event of a public health crisis event, the development of the tertiary sector stagnates, the level of human capital decreases, green investment decreases significantly, and the development of the green economy is hampered . HoweverThe abovementioned literature provides many theoretical bases for this paper to study the impact of public health on green economic efficiency, but there are some shortcomings. Few studies have incorporated environmental regulation, public health, and green economic efficiency into one framework and examined the transmission mechanism of public health events on green economic efficiency in depth. Against the background of the COVID-19 pandemic and the negative GDP growth of the world's major economies, what measures can be taken to promote the growth of green economic efficiency and achieve sustainable economic development remains to be discussed in depth. To this end, this paper applies a four-stage SBM-DEA to measure green economic efficiency and examines the impact of public health events on green economic efficiency in detail at both theoretical and empirical levels. The transmission mechanism of public health events on green economic efficiency is show in In this paper, the energy efficiency index is constructed by a four-stage SBM-DEA.Data envelopment analysis is widely used in efficiency evaluation . CompareStage 1: Input slack and initial energy efficiency values are measured for each decision unit. Since the green economic efficiency is expected to be improved by changing the factor inputs, the input-oriented model is chosen in this paper. Assuming that there are n decision-making units (DMUs), each DMU has m inputs and r outputs, and none of the inputs or outputs is less than zero, the model isx0 and y0 are the input and output vectors of the decision unit to be evaluated, respectively. xi0, yi0 are the elements of x0, y0, where ρ is the efficiency metric; m and k are the input and output factor types, respectively; λ represents column vectors; and Stage 2: Tobit model. After the measurement of efficiency values in the first stage, the amount of slack in the inputs and outputs of each decision unit can be obtained. However, the slack quantity has a value greater than or equal to 0, and there is a truncation in the data when it is equal to 0. Therefore, this paper uses the Tobit truncation model to fit the relationship between input slack quantity and environmental variables in the first stage. Three Tobit regression models are constructed, and the models are defined as follows.i = 1, 2, ..., I; k = 1, 2, ....n. sik represents the total slack of the ith input factor calculated in the first stage, and Zik is the vector of external environment variables, and αi is the constant term, and βi is the vector of coefficients to be estimated, and μi is the random disturbance term.where i is the number of inputs, Stage 3 Decompose the input slack values obtained in one stage using stochastic frontier model (SFA). Construct the regression Equation (2) to decompose the initial input slack values for each decision unit:sik denotes the slack value of the i-th input of the j-th decision unit, zj is the external environment variable, βi is the coefficient of the external environment variable, vij+μij is the mixed error term, vij denotes the random error term, and μij denotes the management inefficiency term.In Equation (2), After using Frontier 4.1 to obtain the regression results, the input quantity of the relatively fully effective decision unit was used as the benchmark, and the input quantity of other relatively ineffective decision units was further adjusted by using the regression results to increase the input quantity of the decision unit in a better external environment to reduce the input quantity of the decision unit facing a worse external environment and probability. The specific method is as follows:ij is the pre-adjusted input, and vij−vij is the adjustment of the random disturbance terms to the same state for all decision units.where XStage 4 Measurement of adjusted SBM efficiency. The adjusted inputs and initial outputs are measured again using the SBM model to derive new efficiency values. Since the interference of external environmental variables is removed in the fourth stage, the efficiency values output in the fourth stage more accurately reflect the actual green economy efficiency level of each decision unit.The specific indicators were selected. The green economic efficiency establishment indicators are shown in Referring to the literature on green economic efficiency indicators measures , we consIn this paper, industrial structure, energy structure, urbanization rate, and R&D investment are selected as environmental variables. Dong  used a sThe core explanatory variable in this paper is public health. In this paper, the mortality rate of legal A and B infectious diseases is selected as the main indicator of public health. In the new infectious disease control law, infectious disease are divided into three categories, A, B, and C. There are 39 types of infectious disease, of which infectious diseases in category B are currently not effectively controlled. Since infectious diseases in category A (plague and cholera) are often considered important factors in public health emergencies, the mortality rate of infectious diseases in categories A and B is selected as a measure in this paper. Referring to the analysis of Lumley and Daly , it is cLi et al.  believe Fixed effects models can capture individual heterogeneity in panel data. The fixed effects model uses panel data to expand the sample size, can describe the individuality and commonality between individuals, and improves the estimation accuracy of the model. The model is set as follows:where GEE denotes green economic efficiency, PHS denotes public health indicators, Z denotes control variables, u is an individual fixed effect, ε denotes error term, i denotes the province, and t is the year.To further test the moderating effect of environmental regulation on the impact of public health on green economy efficiency, a moderated effect estimation model is constructed as follows:where GUI denotes environmental regulation, with the interaction term The data on mortality rates for A and B infectious diseases used in this paper are from the China Health Statistics Yearbook. The data on employment, SO2 emission, secondary industry value added, GDP, and energy consumption were obtained from local statistical yearbooks, the data on total energy consumption were obtained from the China Energy Database, and the data on fixed asset investment, coal consumption, and primary energy consumption were obtained from a wind database. The data on R&D investment is from the China Statistical Yearbook on Science and Technology. Data on urban population, total population, investment in industrial pollution control, government expenditure on science and technology, general budget expenditure, and total imports and export are from the China Statistical Yearbook. The data on carbon emissions are from the China Carbon Accounting Database.Combined with data availability, the sample interval selected in this paper is 2011-2019, and the panel data used in this paper cover 30 provinces due to the absence of some data from the Tibet Autonomous Region as well as Hong Kong, Macao, and Taiwan. The descriptive statistics of each indicator are shown in This paper empirically analyzes the input–output efficiency of the green economic efficiency at the inter-provincial level based on the SBM-DEA model using Stata 16.0 software. The higher value of green economic efficiency represents the superior ability of the province and city to utilize the available resources. The results are shown in From the results of the first stage of efficiency analysis, the following can be ascertained. Without considering environmental variables, the green economic efficiency of all 30 provinces in China from 2011 to 2019 reached 0.8 or more. The regional differences in green economic efficiency among provinces are large, among which Qinghai has a green economic efficiency of 1 in all 9 years. Henan has the lowest average green economic efficiency. The first stage is only an efficiency evaluation under the traditional SBM-DEA model, and although the SBM model can distinguish between effective decision units, it contains interference from environmental and random factors. Therefore, the green economic efficiency measured by the SBM model alone is undoubtedly unrealistic, and the SFA model needs to be applied to remove the influence of external environmental factors.The slack variables of each input variable obtained in the first stage were used as dependent variables and the four environmental variables were used as independent variables, and the Tobit model was constructed using Stata 16.0 software for analysis, and the results are shown in Using the SFA model with the slack variables of labor, energy, and capital inputs obtained in the first stage as explanatory variables and the four environmental variables as explanatory variables in the regression, the results of the third-stage SFA regression can be obtained using Frontier 4.1 software. γ indicates the proportion of the variance of input slack values due to inefficient internal management or input scale in the total variance of input slack values. The larger the effect of internal management or input scale inefficiency on green economy efficiency, the larger the value of this statistic, which indicates that the adjustment of SFA for input variables is reasonable and necessary. For the environmental variables on input, redundancy is regarded as the opportunity cost of production and consumption in each province, that is, when the regression coefficient is positive, it leads to an increase in environmental variables and wastes inputs or decreases outputs, which is not conducive to improving green economic efficiency. Conversely, when the regression coefficient is negative, the increase of environmental variables saves inputs or increases outputs, which is conducive to improving green economic efficiency. The regression results are shown in According to There are differences in the effects of each environmental variable on different provinces, which may lead to better efficiency performance for some provinces facing a better external environment and worse efficiency performance for some provinces facing a worse external environment. Therefore, it is necessary to adjust the original input variables according to the regression results of the second stage, so that all provinces face the same external environment and thus obtain true energy efficiency.The SBM-DEA model was again applied to measure the efficiency based on the adjusted amount of inputs and the initial amount of outputs in each province to obtain efficiency values that reflect the true internal management and input scale levels. The results are shown in The inter-provincial analysis shows that the green economic efficiency of 30 provinces varies to different degrees after excluding the influence of the external environment and random disturbances. This indicates that the external environment and random disturbances have a certain influence on the efficiency level, and the efficiency values measured by each province in the first stage are not very accurate. In general, the green economic efficiency gap is relatively obvious, with Guangxi, Gansu, and Qinghai having the highest average green economic efficiency, indicating that they have a reasonable layout in terms of pollution control and resource utilization efficiency. Shandong has the lowest average green economic efficiency, indicating that the province has a large gap in its green economic efficiency, and should focus on its resource utilization efficiency, environmental protection, and capacity planning.p-values for public health parameter estimates from Models 1 to 5 were all significantly negative at the 1% level. That is, the regression coefficient of public safety on green economic efficiency is always significantly negative. It shows that the occurrence of public security incidents will hinder green economic efficiency. The possible reason for this is that once a public safety event occurs, it can greatly affect everything from micro-individuals to macro-policies. A public safety event can bring about a series of chain reactions. Green industry development stagnates, green investment drops sharply, and human capital level decreases, which in turn greatly hinders green development and green economy efficiency decreases.The estimated results of the panel models are presented in The coefficient of the government's science and technology funding intensity is significantly negative, indicating that the increase in the government's science and technology funding intensity will hinder the efficiency of the green economy. The coefficient of foreign trade intensity is significantly positive, indicating that the increase of foreign trade intensity will promote green economy efficiency. The coefficient of energy price is significantly positive, indicating that the increase of energy price will promote green economic efficiency.*PHS on green economic efficiency is significantly positive at the 1% level. Specifically, a clean and hygienic environment not only prevents the occurrence of serious public health events but also prevents the spread of viruses and bacteria after such events. Environmental protection and public health have public goods characteristics  test] for all GMM regressions, and performs Hansen or Sargan tests. The null hypothesis of the serial autocorrelation test is that there is no serial autocorrelation, and the null hypothesis of the Hansen test and the Sargan test is that the instrumental variables satisfy exogeneity. To ensure model validity, the AR(2) test, Hansen test, or Sargan test with a P value greater than 0.05 is required. The specific regression results of the endogeneity test are shown in Public health has been a topic of great concern, especially in recent years. This article demonstrates whether there is an impact on public health green economy efficiency and the role of environmental regulation in achieving sustainable economic development. In theory, the occurrence of public security incidents will seriously hinder green economic efficiency. This paper empirically tested the path and heterogeneity of the impact of public health events on the efficiency of the green economy by constructing a panel model and an adjustment model.The main conclusions of this paper are as follows: First, public health events have a significant hindering effect on the efficiency of the green economy. The occurrence of public health events will hinder the development of tourism, reduce the level of human capital, and hinder green investment, which will significantly affect the efficiency of the green economy. Second, environmental regulation plays a significant role in regulating the impact of public health events on the efficiency of the green economy. When a public security incident occurs, the government strengthens the intensity of environmental regulation to reduce the possibility of the recurrence of public health crises. With the increase in the intensity of environmental regulation, under the dual pressure of public crisis events and government mandatory policies, enterprises will choose green transformation, reduce pollutant emissions, and save resources for the sustainable development of enterprises, thus promoting green economic efficiency . Third, There are three innovative points in this paper: First, it constructs green economic efficiency indicators by building a four-stage SBM-DEA model. Second, it explores the impact of public health events on green economic efficiency from the perspective of environmental regulation. Third, the impact of public health events on green economic efficiency is explored in terms of geographic location, carbon pilot, and traffic level heterogeneity.In the post-pandemic period, balancing economic development and environmental protection is urgently required. This paper provided the following insights: First, when a public safety event occurs, the government should quickly enter into prevention and control to stabilize the public and build self-confidence to prevent a sharp decline in green investment. Second, it is necessary to increase investment in human capital and improve people's physical resilience, and prevent a significant decline in the level of human capital when a public safety event occurs from hindering the efficiency of the green economy. Third, the intensity of environmental regulations should be increased in a reasonable way to reduce the hindering effect of public health events on green economic efficiency. Fourth, local governments should develop appropriate policies based on local conditions, taking into account local transportation levels, whether they are carbon pilots or their geographical locations.There are also certain research limitations in this paper. First, in the empirical part, it does not verify the transmission mechanism by which public health events affect the efficiency of the green economy through industrial structure, green investment, and human capital level. In the follow-up research, an intermediary model could be constructed to verify the transmission mechanism of public health events affecting green economic efficiency through industrial structure, green investment, and human capital level. Second, this paper does not discuss the spillover effect of public health events on the efficiency of the green economy. Public health events may affect the efficiency of the green economy in adjacent regions. Subsequent research could explore the spillover effect of public health events on green economic efficiency, and verify whether there is a spillover effect through aspatial econometric model.The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding authors.Writing—original draft preparation: JZ. Writing—review and editing: YY, ZF, and KZ. All authors contributed to the article and approved the submitted version.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.


This study builds conceptual explanations and empirical examinations of the vulnerability response of networks under attack. Two quantities of “vulnerability” and “uncertainty in vulnerability” are defined by scrutinizing the performance loss trajectory of networks experiencing attacks. Both vulnerability and uncertainty in vulnerability quantities are a function of the network topology and size. This is tested on 16 distinct topologies appearing in infrastructure, social, and biological networks with 8 to 26 nodes under two percolation scenarios exemplifying benign and malicious attacks. The findings imply (i) crossing path, tree, and diverging tail are the most vulnerable topologies, (ii) complete and matching pairs are the least vulnerable topologies, (iii) complete grid and complete topologies show the most uncertainty for vulnerability, and (iv) hub-and-spoke and double u exhibit the least uncertainty in vulnerability. The findings also imply that both vulnerability and uncertainty in vulnerability increase with an increase in the size of the network. It is argued that in networks with no undirected cycle and one undirected cycle, the uncertainty in vulnerability is maximal earlier in the percolation process. With an increase in the number of cycles, the uncertainty in vulnerability is accumulated at the end of the percolation process. This emphasizes the role of tailoring preparedness, response, and recovery phases for networks with different topologies when they might experience disruption. This, in part, is due to the need to understand the overall system’s response under peculiar circumstances. Malicious and random attacks induced by nature or humans are pertinent examples7. As our daily lives depend on the functioning of networks ranging from infrastructure  to social  and biological , research has proliferated to examine the vulnerability of networks under percolation16.From the six handshakes rule17. Recent events including the spread of COVID-19 through individuals over the networks of contacts in 202018, the shutdown of the New York City subway system following Hurricane Ida in 202119, and the power outage experienced by 2 million Texan households induced by a massive winter storm in 202120 have shown how the vulnerability response of systems exacerbates the effect of attacks on our daily lives, with severe social and economic consequences.Vulnerability is critical when pondering on the ability of a network to provide continuity in its operation. It refers to the magnitude of network performance loss relative to its pre-disruption performance in the presence of disruptions and the absence of response resources25. It includes sequential single link removal26, sequential multiple link removal7, randomly chosen multiple link removal6, and targeted multiple link removal6. Examples of examining the vulnerability of networks under random, targeted, and cascading disruptions15 exist in traffic networks 16, public transit networks 7, power grid networks 5, and complex networks 15. Little is known about the vulnerability response of networks with different topologies and sizes under different attack scenarios. This study is a natural continuation of previous research and contributes to understanding the vulnerability response of networks by (i) introducing the concept of “uncertainty in vulnerability” and (ii) visualizing and measuring the vulnerability of networks with different topologies and sizes when links are removed in order of their degrees. This happens by starting with the highest degrees and working down, then using the lowest degrees and working up while recalculating the residual network flow in each iteration.Much of the previous research has contributed to examining the vulnerability of networks through the lens of percolation in which links are removed or become non-functional uniformly at random or in order of their degreesHere, our overarching goal is to equip scientists and practitioners with the knowledge and tools necessary to understand the vulnerability response of networks in relation to the network topology. We define two quantities to characterize the vulnerability response. The first quantity, We define network mentclass2pt{minimFollowing the disruption of 27. Here, we do not exercise this condition as we assume a uniform fixed link cost and uniform demand. This assumption, however, is not restrictive as our algorithm generates two non-inferior trajectories that postulate the performance bounds under benign and malicious attacks. These proposed bounds encompass the performance loss trajectory of network topologies with different link characteristics.A peculiar condition is when Equation  mathematWhen entclass1pt{minimaThe maximum value of The minimum value of The following considerations are important:Following the relative performance and redundancy definition, we formally define vulnerability under benign and malicious attacks in Eqs.  and 4),,4), wherImmediately, the uncertainty in vulnerability can be introduced by Eq. . This is. The malicious and benign attack scenarios are respectively linked to the maximum and minimum performance loss rate in each link removal step. We employ both attack scenarios on a range of network sizes from 8 to 26 nodes. Although this range is noted in existing analysis of actual networks with examples of transport networks29, gas networks30, power networks31, and water networks32, it is selected to exemplify how vulnerability and uncertainty in vulnerability is a function of the size of the network. We document the generalization of our findings for 16 network topologies with more than 26 nodes in Supplementary Information We visualize the performance loss trajectory of network disruptions for 16 topologies with different sizes in physical, social, meteorological, and biological systems documented in Supplementary Information IIFigure A similar examination on uncertainty in vulnerability leads to conclusive findings derived from Fig. We argue that uncertainty in vulnerability is not a uniform area and is a function of the topology, as observed in Fig. Figure .We prove that the vulnerability quantity falls into the interval In small-sized networks with 8 nodes, it is observed that all topologies are in either LL or HL, with the complete grid topology as an exception. This means the uncertainty in the vulnerability of networks is low regardless of the topology. In particular, it is observed that (i) diverging tail, crossing path, tree, double u, ring, central ring, converging tail, grid, and random topologies locate in the HL region, (ii) diamond, scale-free, matching pair, single depot, complete, and hub-and-spoke fall in the LL region, and (iii) complete grid resides in the LH region. No network topology is detected in the HH region for networks with 8 nodes. With an increase in the size of the network, a steady increase in both vulnerability and uncertainty in vulnerability is recognized to the extent that no network topology remains in the LL region. The rate of escalation, however, depends on the network topology. The lowest rate goes to hub-and-spoke with a slight increase in vulnerability and no change in uncertainty in vulnerability when there is an increase in the size of the network. The highest shift is noticed for the diamond topology, which moves from the LL region to the HH region.For the grid topology, The complete grid network topology closely resembles the complete topology. Mathematically, we show the resemblance by measuring the difference between For the diamond topology, we notice that the network size increases the number of redundant links by Diverging tail, crossing path, tree, double u, ring, central ring, converging tail, and single depot remain in the HL region. Still, the vulnerability and uncertainty in vulnerability increase with an increase in the size of the network. Grid, complete grid, and diamond move to the HH region as the network size increases. This shift is due to the ascending increase in the number of links with an increase in the size  of the network as illustrated by the A similar pattern is noticed for the scale-free network topology. The scale-free topology switches from LL to the HH region as the network size increases. We speculate that the shift is due to the positive correlation between the number of hubs and the size of the network in the scale-free topology. An increase in the number of hubs increases the disruption scenario alternatives and the uncertainty in vulnerability. Matching pair, complete, and random network topologies move to the LH region as they experience a higher increase in uncertainty in vulnerability than in vulnerability with an increase in the size of the network.Without in-depth knowledge of the network response under attacks, there is a risk of underestimating the stochasticity of disruptive impacts on the network performance. This might cause a loss of control over the network devolution trajectory, and makes room for unexpected cascading failures like what was induced by a massive winter storm in Texas in 2021. Understanding the complexity of network response under attack calls for a holistic approach to visualize and quantify the vulnerability trajectory of networks when experiencing the loss of performance. We have introduced two quantities of vulnerability Ipso facto, uncertainty in vulnerability is not necessarily a function of vulnerability when different topologies are considered. We have recognized that complete grid and complete topologies show the most uncertainty in vulnerability, unlike hub-and-spoke and double u. Similar to the vulnerability, uncertainty in the vulnerability of networks increases with an increase in the size of the network. This finding has practical implications in network inauguration or expansion as it provides insights on (i) how the vulnerability of a network topology changes with an increase in the size and (ii) how the vulnerability of a network can be regulated by shepherding the network growth into the desired topology.Ranking network topologies by their vulnerability, we have determined crossing path, tree, and diverging tail are the most vulnerable networks. At the same time, complete and matching pairs exhibit almost the lowest vulnerability under the malicious attack. The largest gap in vulnerability exists between tree and complete topologies to the extent that the vulnerability of the tree topology is almost 2 times the complete topology. We have also determined that the vulnerability of networks increases with an increase in the size of the network and notice a slight change in the vulnerability ranking of networks. Ranking network topologies by their uncertainty in vulnerability have indicated a low correlation between our two quantities. The findings have demonstrated that the vulnerability response of networks to an increase in size falls into two categories depending on the network’s topology. For the first category, vulnerability increases at a faster rate than the corresponding uncertainty in vulnerability. The hub-and-spoke and single depot topologies are the only examples. The uncertainty in vulnerability of the hub-and-spoke topology equals zero regardless of the network size. For the second category, uncertainty in vulnerability increases at a faster rate than the corresponding vulnerability. The remaining network topologies, except the random topology, fall in this category. As suggested by its name, random is the only topology with unstable behavior. Although the uncertainty in vulnerability increases with an increase in the size of random networks, their vulnerability fluctuates and is not a function of the size.Depending on the network topology, the structure of the residual network may or may not change under percolation. For instance, the tree and ring topologies maintain and lose their configuration, respectively, under percolation in which links are removed at random or in order of their degrees. A tree network with 8 nodes and 7 links shrinks to two tree topologies following a link removal. However, a ring network with 8 nodes and 8 links metamorphoses into a tree network with 7 links following a link removal. This leads the performance loss trajectory of networks to diverge or converge under benign and malicious attacks over the percolation process, forming a heterogeneous uncertainty in vulnerability. It means the area between the upper and lower bounds of performance loss trajectories does not shrink or expand continually when links are removed in order of their degrees. We have argued that the contour of the area is a function of the network topology, and the number of cycles explains the heterogeneous uncertainty in vulnerability formed over the percolation process. In networks with no undirected cycle, the uncertainty in vulnerability is maximum earlier in the percolation process. Diverging tail, tree, and crossing paths are three examples. Interestingly, they also exhibit the highest vulnerability. With an increase in the number of cycles, the uncertainty in vulnerability is accumulated at the end of the percolation process. An extreme example is detected in complete, matching pair, and random topologies. Interestingly, they also exhibit the lowest vulnerability. Hence, we have indicated a negative correlation between the vulnerability and network circuity estimated by This immediately has practical implications. Not only are tree, crossing path, and diverging tail the most vulnerable topologies, but they also exhibit the highest uncertainty in performance loss earlier in the process when they experience a random attack. This emphasizes the time sensitivity of maintenance and recovery of tree, crossing path, and diverging tail topological systems when they are under attack and the role of preparedness to avoid the spread of the attack. We take post disruption casualty evacuation as a pertinent example of implementing these implications in transport networks. Here, the search and rescue teams can identify the affected areas with topologies resembling tree, crossing path, and diverging tail as more probable to contain trapped residents. The reason is that all routes out of the affected areas can be disrupted faster than expected. Relying on such inferences, the teams prioritize the emergency deployment across these areas. Conversely, complete and matching pair networks are the least vulnerable topologies but exhibit a wider range of uncertainty in vulnerability at a later stage under a random attack. This is alarming. We analogize them to dormant volcanoes. They might not cause any concern when they are attacked, but they experience a remarkable performance loss as the attack continues and links become unfunctional one by one. This emphasizes the role of protection during the attack. Protecting transport networks under a limited budget provides another pertinent example of using these inferences in the interest of infrastructure network resilience. Planners and emergency managers can identify the minimum number of paths__ if protected__ that can maintain the transport network performance under random attacks. The optimal protection policy enhances the evacuation procedure and reduces the subsequent humanitarian logistics costs.Potential avenues remain for future research leading to intriguing additional questions that connect the theoretical explorations in this work to real-world networks in specific domains. First, we have considered networks under uniform demand, while most real-world networks exhibit demand patterns with higher-density axes over both time and space and reflect underlying demand patterns. Although our analysis provides a basis for comparison, it might underestimate or overestimate vulnerability or exaggerate it for links intended for higher flows than links designed to ensure basic access. An extension of this work would consider expanding the notion of uncertainty in vulnerability to incorporate variability in demand patterns . Second, we have adopted the linear programming for maximum throughput allocation, as flow allocation rules in most networks tend to follow some sort of optimal principle. In certain networks, however, flow allocation follows significantly different principles, such as user-optimized flow rules in congestible transport networks. Third, we have considered networks with unlimited link capacity, whereas, in practice, capacity constraints often lead to progressive failure. The existence of capacitated links affects the post-disruption flow redistribution and changes the performance degradation trajectory and, consequently, the vulnerability bonds. While the new bounds fall into our proposed vulnerability bounds, their patterns will provide information about the trajectory of uncertainty in the vulnerability of capacitated networks, including the magnitude and number of sudden performance degradations. Fourth, we have produced our analysis under the link percolation assumption. While much of the literature has focused on link percolation, equally important is node percolation, which would debilitate many links simultaneously. This is especially acute for certain topologies such as hub-and-spoke networks, where an attack on hub nodes could make an entire network unfunctional.The proposed formulation maximizes the total delivered demand in the residual network. In a network with As we assume one unit of demand is transferred between each origin–destination pair, the total flow passing each link is the same as its betweenness centrality. We represent Equation  represenEquation  sends onEquation  calculatTwo greedy algorithms are proposed to explore the sequence of link removal procedures that respectively (i) maximizes the total unsatisfactory demand after the removal of each link, also called a malicious attack simulation, and (ii) minimizes the total unsatisfactory demand after the removal of each link, also called a benign attack. The input of each algorithm is the topological characteristics and the flow on each link at the original state. After removing a link, the flow is redistributed through the residual network. The procedure repeats until no link remains undisrupted. The Malicious-Benign Attack Simulation algorithm is as follow:Supplementary Information.