Mauritius stands as one of the few countries in the world to have controlled the current pandemic, the novel coronavirus 2019 (COVID-19) to a significant extent in a relatively short lapse of time. Owing to uncertainties and crisis amid the pandemic, as an emergency announcement, the World Health Organization (WHO) solicits the help of health authorities, especially, researchers to conduct in-depth research on the evolution and treatment of COVID-19. This paper proposes an integer-valued time series model to analyze the series of COVID-19 cases in Mauritius wherein the corresponding innovation term accommodates for covariate specification. In this set-up, sanitary curfew followed by sanitization and sensitization campaigns, time factor and safe shopping guidelines have been tested as the most significant variables, unlike climatic conditions. The over-dispersion estimates and the serial auto-correlation parameter are also statistically significant. This study also confirms the presence of some unobservable effects like the pathological genesis of the novel coronavirus and environmental factors which contribute to rapid propagation of the zoonotic virus in the community. Based on the proposed COM-Poisson mixture models, we could predict the number of COVID-19 cases in Mauritius. The forecasting results provide satisfactory mean squared errors. Such findings will subsequently encourage the policymakers to implement strict precautionary measures in terms of constant upgrading of the current health care and wellness system and re-enforcement of sanitary obligations.