Global stability and optimal control of SIRS model with media coverage: analysis of infected and susceptible population

Abstract

In this paper a system of SIRS epidemic model with media coverage is considered. We perform a study of global stability analysis, and sensitivity analysis of the basic reproduction number R₀. The system is globally asymptotically stable about the endemic equilibrium if the basic reproduction number R₀ > 1. The geometric approach is used to prove the global stability of the endemic equilibrium if the basic reproduction number R₀ > 1. R₀ depends on a set of positive parameters. The sensitivity indices of those parameters are calculated by using the normalized sensitivity formula and can be classified into two classes: one class has a positive correlation with R₀, and the other class has a negative correlation with R₀. Furthermore, Optimal control is applied to explore the possible control strategies to prevent disease spread in the community. We extend the proposed SIRS model to include three control variables namely educational campaign, vaccination, and treatment care. Using Pontryagin’s maximal principle, we established the necessary conditions for the existence of optimal control. We use the fourth-order Runge Kutta forward-backward sweep approach to simulate the optimality system in order to demonstrate the impact of various combinations of controls on the spread of disease. A cost-effectiveness study is carried out to inform the public about the best cost-effective technique among several control combinations. The results suggest that, the preventative tactics through educational campaigns is the most cost-effective.