Optimal control for a discrete time epidemic model with zones evolution

Abstract

In this paper, we present a new mathematical model to describe the evolution of an infectious disease in regions and between individuals. For this purpose we considered two systems, the first one for humans S_iI_iR_i, where Si represents the number of susceptible, I_i of infected and Ri of cured. The second system Z^S_i Z^I_iZ^R_i represents the different types of regions, where Z^s_i is the number of susceptible regions, where there are only susceptible people, after visiting an infected person, a susceptible region is likely to be infected, which we will note Z^I_i, the last compartment Z^R_i denotes the infected regions, which are restored after the recovery of all infected people. In addition, we considered three control strategies u, v and w to control the spread of the virus within regions and between individuals. Numerical examples are provided to illustrate the effectiveness of our proposed control strategy.