Global stability analysis of an epidemic model with feedback control and general incidence rate

Abstract

In this paper, SIR model with feedback control has been considered. By constructing the Lyapunov function, using the Routh–Hurwitz criterion and the positive definite quadratic form theory, some sufficient conditions have been obtained, and some well-known results have been generalized. It is worth mentioning that if the feedback control variables have an inhibitory effect on the susceptible population and the infected population, the number of basic regeneration of the disease will be reduced. The reduction depends only on the control of the susceptible population, but not on the control of the infected population. This is a very interesting conclusion.