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

Nidhal Faisal  Ali; Hassan F.  Al-Husseiny

doi:10.24996/ijs.2025.66.1.%g

Authors

Nidhal Faisal Ali Department of electrical Engineering Techniques, College of Electrical Engineering Technical, University Middle Technical, Baghdad/Iraq
Hassan F. Al-Husseiny Department of Mathematics, College of Science, University of Baghdad, Baghdad , Iraq

DOI:

https://doi.org/10.24996/ijs.2025.66.1.%25g

Keywords:

Infection diseases, Stability, Time delay, Hopf bifurcation

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.