1. Stability Switches, Hopf Bifurcation and Chaotic Dynamics in Simple Epidemic Model with State-Dependent Delay.
- Author
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Qesmi, Redouane, Heffernan, Jane M., and Wu, Jianhong
- Subjects
HOPF bifurcations ,BIFURCATION diagrams ,EPIDEMICS ,STABILITY criterion ,COMMUNICABLE diseases ,TORUS - Abstract
Dynamic behavior investigations of infectious disease models are central to improve our understanding of emerging characteristics of model states interaction. Here, we consider a Susceptible-Infected (SI) model with a general state-dependent delay, which covers an immuno-epidemiological model of pathogen transmission, developed in our early study, using a threshold delay to examine the effects of multiple exposures to a pathogen. The analysis in the previous work showed the appearance of forward as well as backward bifurcations of endemic equilibria when the basic reproductive ratio R 0 is less than unity. The analysis, in the present work, of the endemically infected equilibrium behavior, through the study of a second order exponential polynomial characteristic equation, concludes the existence of a Hopf bifurcation on the upper branch of the backward bifurcation diagram and gives the criteria for stability switches. Furthermore, the inclusion of state-dependent delays is shown to entirely change the dynamics of the SI model and give rise to rich behaviors including periodic, torus and chaotic dynamics. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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