A robust Study of the Treatment Delay Effect on the Dynamics of Epidemic Disease

Nidhal Faisal Ali; Hassan F. Al-Husseiny

doi:10.24996/ijs.2024.65.2.29

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.2024.65.2.29

Keywords:

Infection diseases, Stability, Time delay, Hopf bifurcation, Treatment function

Abstract

A general treatment function with an epidemic model that involves the delay in the treatment period has been proposed and studied in this work. This model contains two compartments, namely susceptible denoted by and infected denoted by . The existence of all the fixed points has been determined. The system has two equilibrium points, namely the uninfected equilibrium point (UIEP) and the endemic equilibrium point (EEP). The conditions for local stability and Hopf bifurcation have been discussed. The stability of the periodic solutions and the direction of the Hopf bifurcation properties have been studied analytically and numerically.