Abstract
This research introduces an expanded SEIR (Susceptible-Exposed-Infected-Recovered) model that incorporates the components of testing, treatment, and vaccination. The study utilizes an evolutionary game theory (EGT) framework to investigate the impact of human behavior on the acceptance and implementation of these interventions. The choice to undergo testing and vaccination is considered a strategic decision influenced by perceived risks and benefits. Regarding disease dynamics, adherence to vaccination and testing protocols is seen as a behavioral factor. The present study employs a finite difference method to numerically examine the impact of proactive vaccination and retroactive treatment policies on human behavior. The investigation focuses on these policies' individual and combined effects, considering various factors, including vaccination and testing costs, vaccine efficacy, awareness level, and infection rates. The findings indicate that the integration of heightened awareness and enhanced vaccination efficacy can successfully alleviate the transmission of diseases, even in situations where the expenses associated with testing and vaccination are substantial. Reducing infections in situations characterized by low or moderate awareness or vaccination effectiveness is contingent upon low testing costs. The final epidemic size (FES) negatively correlates with testing and vaccine costs, indicating that lower costs are linked to a lower FES. Optimal vaccine coverage (VC) occurs when vaccine costs are minimal and vaccine efficiency is efficient, whereas treatment coverage (TC) reaches its peak when testing costs are minimal. This research underscores the significance of considering human behavior and the intricate relationship between vaccination, testing, and treatment approaches in managing the transmission of contagious illnesses. It offers valuable perspectives for policymakers to mitigate the consequences of epidemics.