混乱的
霍普夫分叉
分叉
数学
分岔图
跨临界分岔
理论(学习稳定性)
分叉理论的生物学应用
倍周期分岔
工作(物理)
控制理论(社会学)
应用数学
基本再生数
统计物理学
计算机科学
物理
非线性系统
人口
控制(管理)
人口学
量子力学
人工智能
机器学习
社会学
热力学
作者
Redouane Qesmi,Jane M. Heffernan,Jian Wu
标识
DOI:10.1142/s0218127423300288
摘要
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 [Formula: see text] 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.
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