A multi-regions SEIS discrete epidemic model with a travel-blocking vicinity optimal control approach on cells

Abstract

In Susceptible-Exposed-Infected-Susceptible (SEIS) compartmental models, an infected population is divided into two categories; symptomatic infected individuals represented by the I variable, and asymptomatic infected individuals, people who are not yet infectious, or those who are just exposed to infection, represented by the variable E. In these models, an infected population recovers with no immunity, and then, it moves immediately to the susceptible compartment once it becomes recovered, For this, we devise a multi-regions SEIS discrete-time model which describes infection dynamics when an epidemic is emerging in regions that are connected with their neighbors by movement. The main goal from this kind of modeling, is to introduce after, controls variables which restrict movements of the infected individuals coming from the vicinity of the region targeted by our control strategy, called here; the travel-blocking vicinity optimal control approach. A grid 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 corners of the grid, while the region aiming to control, is supposed to be located in the 4th line and 7th column of the grid, as an example to show the effectiveness of the proposed control strategy when it is applied to a cell with 8 neighboring cells.