A Multi-Regions SIRS Discrete Epidemic Model With a Travel-Blocking Vicinity Optimal Control Approach on Cells

In Susceptible-Infected-Removed-Susceptible (SIRS) compartmental models, we can suppose that a removed population has lost its immunity after being healed from an infection, and then, it moves to the susceptible compartment. In this paper, we devise a multi-regions SIRS discrete epidemic model which describes infection dynamics in regions which are connected with their neighbors by any kind of anthropological movement. We introduce controls variables into our model to show the effectiveness of movements restrictions of the infected individuals coming from the vicinity of a region we target by a control strategy we call here by the travel-blocking vicinity optimal control strategy. A gridded surface of colored cells is presented to illustrate the whole domain affected by the epidemic while each cell represents a sub-domain or region. The infection is supposed starting from only one cell located in one of the borders of the surface, while the region aiming to control is supposed to be located in the center as an example to show the effectiveness of the travel-blocking vicinity optimal control approach when it is applied to a cell with 8 neighboring cells.