Dynamical behaviors and social efficiency deficit analysis of an epidemic model with three combined strategies

In this article, we develop an SuSaVITR epidemic model that incorporates three unique behavior dynamics based on the evolutionary game theory (EGT). This study includes some of the most effective strategies for controlling the COVID-19 epidemic such as awareness, vaccination, and treatment, all of which depend on changes in human behavior influenced by risk perception and careful evaluation of costs. Each intervention in the behavioral model is represented by a dynamic equation that balances the associated costs against the risk of infection. In the non-behavioral model, we use the normalized forward sensitivity index method for local sensitivity analysis of the basic reproduction number (R0), while the LHS-PRCC method is employed for global sensitivity analysis of the infected compartment to identify the most influential parameters affecting disease dynamics. The simultaneous application of three strategies incorporating EGT with the minimum possible cost for each intervention proves to be the most effective approach for reducing the maximum number of infections compared to the application of single or double strategies. Simultaneously, the numerical results show that when awareness effect, vaccine efficacy and treatment recovery rates are high, they can significantly reduce the community’s risk of infection. Also, the average social payoff has been evaluated at both Nash equilibrium and social optimum to emphasize the increased social benefits that emerge when the costs of awareness, vaccination and treatment are minimized. Finally, the social efficiency deficit has been discussed to identify the situations that lead to dilemmas related to the epidemic model.