An in-silico game theoretic approach for health intervention efficacy assessment

The global rise of multi-strain epidemics has raised significant concerns in the field of public health. To address this, our research introduces a game-theoretic approach to predict the evolutionary dynamics of multi-strained pathogens. Our proposed model sheds light on the pivotal role of vaccination in controlling the growth of such infectious diseases. Here, we propose a modified Susceptible-Vaccinated-Infected-Recovered (SVIR) model featuring two strains and corresponding vaccines: one is the primary vaccine that is designed to target the original strain (effectiveness: $e_1$) and simultaneously exhibits some effectiveness against the mutant strain ($e_2$), another is the mutant vaccine that concentrates on the mutant strain (${\eta }_2$) while showing significant effectiveness against the primary strain (${\eta }_1$). Next, we present a comprehensive time series analysis to examine the fraction of the vaccinated population who adopted these two vaccines. This work elucidates that with a slight increase effectiveness- setting $e_1=0.5$, $e_2=0.3$, ${\eta }_1=0.6$, and ${\eta }_2=0.7$- the mutant vaccine works more proficiently under both imitation dynamics known as Individual-Based Risk Assessment (IB-RA) and Strategy-Based Risk Assessment (SB-RA). Furthermore, a detailed analysis comparing these two imitation dynamics is demonstrated and also to reconcile the matter that the Strategy-Based-Risk-Assessment process should be adopted to minimize epidemic size. Finally, considering individuals’ attitudes and behaviors towards vaccination, we introduce a replicator equation. Subsequently, a thorough examination of the relationship between imitation dynamics and behavioral dynamics is presented where imitation dynamics outstripped behavioral dynamics which is confirmed by the use of heat maps.