Qualitative Analysis and Optimal Control Strategy of an SIR Model with Saturated Incidence and Treatment

TL;DR

This paper analyzes an SIR epidemic model with saturated incidence and treatment, exploring equilibrium stability, bifurcations, and optimal control strategies to effectively reduce disease spread.

Contribution

It introduces a comprehensive analysis of an SIR model with saturated effects and develops an optimal control framework using Pontryagin's maximum principle.

Findings

Vaccination and treatment controls effectively reduce infection levels.

Optimal strategies depend on model parameters and control costs.

Numerical results demonstrate the positive impact of combined control measures.

Abstract

This paper deals with an SIR model with saturated incidence rate affected by inhibitory effect and saturated treatment function. Two control functions have been used, one for vaccinating the susceptible population and other for the treatment control of infected population. We have analysed the existence and stability of equilibrium points and investigated the transcritical and backward bifurcation. The stability analysis of non-hyperbolic equilibrium point has been performed by using Centre manifold theory. The Pontryagin's maximum principle has been used to characterize the optimal control whose numerical results show the positive impact of two controls mentioned above for controlling the disease. Efficiency analysis is also done to determine the best control strategy among vaccination and treatment.