Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan.
Faculty of Education, Tokyo Gakugei University, 4-1-1 Nukuikita-machi, Koganei-shi, Tokyo 184-8501, Japan.
Math Biosci Eng. 2023 Jun 5;20(7):13036-13060. doi: 10.3934/mbe.2023581.
In this paper, we examine the stability of an endemic equilibrium in a chronological age-structured SIR (susceptible, infectious, removed) epidemic model with age-dependent infectivity. Under the assumption that the transmission rate is a shifted exponential function, we perform a Hopf bifurcation analysis for the endemic equilibrium, which uniquely exists if the basic reproduction number is greater than 1. We show that if the force of infection in the endemic equilibrium is equal to the removal rate, then there always exists a critical value such that a Hopf bifurcation occurs when the bifurcation parameter reaches the critical value. Moreover, even in the case where the force of infection in the endemic equilibrium is not equal to the removal rate, we show that if the distance between them is sufficiently small, then a similar Hopf bifurcation can occur. By numerical simulation, we confirm a special case where the stability switch of the endemic equilibrium occurs more than once.
本文研究了一个具有年龄相关传染性的时变年龄结构 SIR（易感、感染、移除）传染病模型中地方病平衡点的稳定性。在假定传播率为移位指数函数的假设下，我们对地方病平衡点进行了 Hopf 分支分析，如果基本再生数大于 1，则该平衡点唯一存在。我们证明，如果地方病平衡点的感染率等于移除率，那么当分支参数达到临界值时，总是存在一个临界值，从而发生 Hopf 分支。此外，即使在地方病平衡点的感染率不等于移除率的情况下，我们也证明，如果它们之间的距离足够小，则可能会发生类似的 Hopf 分支。通过数值模拟，我们证实了地方病平衡点的稳定性开关发生多次的特殊情况。
