On Building Two-Player Games with Treatment Schedules for the SIR Model

Abstract

In this study, a treatment argument is provided as a discrete two-player game related to an epidemiological dynamics, so-called, Susceptible- Infectious-Recovered (SIR) model. Here, a simple discrete version of the dynamics of SIR model is considered within a treatment structure in such a way to control the behaviour of each candidate: population of the susceptible, infected and recovered people, respectively. In this regard, several two-player game models are proposed, where one player follows its own existed policy where as the other tries to track its opponent's treatment schedule as close as possible. In this regard, different strategies are built for one player to catch the other in a two-player game environment, where one player determines the total number of susceptible or infected people at a given period, in the meantime, the other tries to build its corresponding treatment policy to get closer to its opponent's counting schedule. The main contribution of this work is to build a better treatment schedule by using a game theoretical point of view to cure the population suffered from an infectious disease. At the end, the work is related to pursuer-evasion discrete games and the idea could be implemented on compartmental models like COVID-19 and transportation problems.