Complex dynamics in a discrete SIS epidemic model with Ricker-type recruitment and disease-induced death
Complex dynamics in a discrete SIS epidemic model with Ricker-type recruitment and disease-induced death
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DOI：
10.1007/s11071-021-06444-w
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发表时间：
2021-05
影响因子：
5.6
通讯作者：
Lei Xiang;Yuyue Zhang;Jicai Huang;S. Ruan
中科院分区：
文献类型：
--
作者：
Lei Xiang;Yuyue Zhang;Jicai Huang;S. Ruan
本文研究了一类具有Ricker型招募和疾病致死的离散SIS传染病模型的复杂动力学。证明了该模型存在唯一的无病平衡点和唯一的地方病平衡点。得到了平衡点局部渐近稳定的充分条件。在地方病平衡点的详细分支分析表明，随着参数的变化，模型经历了一系列的分支，包括跨临界分支、翻转分支和Neimark-Sacker分支。通过各种数值模拟，包括分岔图、相图、最大Lyapunov指数和可行集，模拟了复杂的周期窗口、周期-28点、多个混沌带、分形池边界、混沌吸引子以及周期点和三个不变环面的共存，不仅说明了理论结果，而且揭示了模型更为复杂的动力学行为。
In this paper, we investigate the complex dynamics in a discrete SIS epidemic model with Ricker-type recruitment and disease-induced death. It is shown that the model has a unique disease-free equilibrium if the basic reproduction numberand a unique endemic equilibrium if. Sufficient conditions for the locally asymptotic stability of the equilibria are obtained. A detailed bifurcation analysis at the endemic equilibrium reveals that the model undergoes a sequence of bifurcations, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation, as the parameters vary. Various numerical simulations, including bifurcation diagrams, phase portraits, maximum Lyapunov exponents and feasible sets, are carried out to present complex periodic windows, period-28 points, multiple chaotic bands, fractal basin boundaries, chaotic attractors and the coexistence of period points and three invariant tori, which not only illustrate the theoretical results but also demonstrate more complex dynamical behaviors of the model.