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 SiIiRi, where Si represents the number of susceptible, Ii of infected and Ri of cured. The second system ZSi ZIiZRi represents the different types of regions, where Zsi 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 ZIi, the last compartment ZRi 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.
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