Dynamics of an SIRS model with age structure and two delays
Dynamics of an SIRS model with age structure and two delays
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具有年龄结构和两次延迟的 SIRS 模型的动力学
DOI：
10.1142/s179352452150056x
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发表时间：
2021-05
影响因子：
2.2
通讯作者：
朱章生
中科院分区：
文献类型：
--
作者：
孙洪全;李红;李进;朱章生
本文提出并研究了一个具有年龄结构和两个时滞的SIRS模型。感染者和恢复者都具有年龄结构，感染率(从感染者到易感者)和免疫损失率(从恢复者到易感者)分别与两个独立的时间延迟有关。我们利用[公式：见正文]-半群理论证明了所提出的年龄结构SIRS模型是适定的。给出了基本繁殖数[公式：见正文]，当[公式：见正文]时存在唯一的地方病平衡，而无病平衡总是存在的。对两个平衡点的稳定性进行了严格的数学分析。如果[公式：见文本]，则无病平衡点是局部渐近稳定的；如果[公式：见文本]和[公式：见文本]，则地方病平衡点是局部渐近稳定的。最后，我们给出了数值模拟来验证我们的结果。
In this paper, we propose and investigate an SIRS model with age structure and two delays. Both the infected and the recovered individuals have age structure, the infection rate (from the infective to the susceptible) and the immune loss rate (from the recovered to the susceptible) are related to two independent time delays, respectively. We prove that the proposed age structured SIRS model is well-posed by using the [Formula: see text]-semigroup theory. The basic reproduction number [Formula: see text] is given, and the unique endemic equilibrium exists when [Formula: see text], while the disease-free equilibrium always exists. A rigorous mathematical analysis for the stability of two equilibria is provided. The disease-free equilibrium is local asymptotically stable if [Formula: see text], and the endemic equilibrium is local asymptotically stable if [Formula: see text] and [Formula: see text]. Finally, we give numerical simulations to verify our results.