Stability of a Time Delayed SIR Epidemic Model Along with Nonlinear Incidence Rate and Holling Type-II Treatment Rate

Abstract

In this paper, we present a mathematical study of a deterministic model for the transmission and control of epidemics. The incidence rate of susceptible being infected is very crucial in the spread of disease. The delay in the incidence rate is proved fatal. In the present study, we propose an SIR mathematical model with the delay in the infected population. We are taking nonlinear incidence rate for epidemics along with Holling type II treatment rate for understanding the dynamics of the epidemics. Model stability has been done by the basic reproduction number [Formula: see text]. The model is locally asymptotically stable for disease-free equilibrium [Formula: see text] when the basic reproduction number [Formula: see text] is less than one ([Formula: see text]). We investigated the stability of the model for disease-free equilibrium at [Formula: see text] equals to one using center manifold theory. We also investigated the stability for endemic equilibrium [Formula: see text] at [Formula: see text]. Further, numerical simulations are presented to exemplify the analytical studies.