Modeling the Influence of Time Delay in Controlling Infectious Diseaseswith A Stage-Structure

Abstract

This research aims to construct a stage-structured mathematical model to evaluate the impact of time delay on infectious disease control. The solution's characteristics are described. Every possible equilibrium point has been determined. The local stability of all equilibrium points for time delay values is investigated. It has been shown that the Hopf bifurcation takes place in the vicinity of the endemic equilibrium point. The periodic dynamics' stability and direction are investigated. Numerical simulations were provided to confirm the theoretical findings and understand the effects of varying parameter values.