Partial Differential Equations in Zero-Sum Differential Game and Applications on Coronavirus

Abstract

In this paper, we studied a zero-sum game described by the partial differential equations as an application on Coronavirus. The game contains two players, player 1 is Coronavirus and player 2 is the population. We used ∞-Laplacian which is denoted by ∆∞. We added the time variable to the partial differential equation to see the behaviour of the spreading of Coronavirus. We used analytical methods, the Homotopy Perturbation Method and New Iterative Method, for solving the partial differential equation. A comparison between the two methods to the residual error is made. We showed in the graph the decreasing of spreading for Coronavirus with increasing the area with the time.