OPTIMAL CONTROL FOR A DISCRETE TIME EPIDEMIC MODEL WITH ZONES EVOLUTION

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 SiIiRi, where S-i represents the number of susceptible, I-i of infected and R-i of cured. The second system Z(i)(S)Z(i)(I)Z(i)(R) represents the different types of regions, where Z(i)(S) 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(i)(R) 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.