An SIR Model with Nonlinear Incidence Rate and Holling Type III Treatment Rate

Abstract

We propose a mathematical model with nonlinear incidence rate and treatment rate to study the dynamics of susceptible-infected-recovered population. We consider nonlinear incidence rate as Crowley-Martin type and nonlinear treatment rate as Holling type III (saturated treatment function). The global stability analysis of disease-free equilibrium point and endemic equilibrium point has been investigated using Lasalles’ invariance principle and Lyapunov function. A threshold value has been found to ensure the extinction or persistence of infection. The non-existence of periodic solutions have been shown using Dulac’s criterion. Numerical simulations are performed to validate these analytical findings.