Stability and optimal control analysis of an SCIR epidemic model

Abstract

In this paper, we proposed a deterministic model of SCIR governed by a system of nonlinear differential equations. Two equilibria (disease-free and endemic) are obtained and the basic reproduction number R₀ is calculated. If R₀ is less than one, then the disease-free equilibrium state is globally stable i.e. the disease will be eradicated eventually. However, when R₀ is greater than unity, the disease persists and the endemic equilibrium point is globally stable. Furthermore, the optimal control problem is applied into the model. The focus of this study is to determine what control method can be implemented to significantly slow the incidence of the epidemic disease, therefore we take into account various possible combinations of such three controls which are prevention via proper hygiene, screening of the infected carriers which enable them to know their health conditions and to go for early treatment and treatment of the infected individuals. The possible strategies of using combinations of the three controls on the spread of the disease, one at a time or two at a time is also discussed. Our numerical analysis of the optimal approach suggests that the best method is to incorporate all three controls in order to control the disease epidemic.