Stability analysis and optimal control of SEIRS mathematical model

Abstract

In this paper, a SEIRS mathematical model for the dynamics of an infectious disease is formulated. That incorporates both the symptomatic and asymptomatic individuals. The evolution of a contagious disease is done by contact with infectious persons and susceptible persons. In this work we consider SEIRS mathematical model with variable contact. The mathematical study of the model is made by calculating the basic reproduction number R 0 and by studying the global stability of the equilibrium points.Our model takes into consideration the control of contact (γ) between infectious individuals and susceptible persons. In addition, the optimal control u represents any preventive measure of COVID-19 such as vaccination. The objective is to reduce the contact between the infectious persons and the susceptible persons or decrease the contact effect between then by using vaccination. The numerical simulation of the model is made to illustrate the theoretical results.