具有饱和发生率的确定性和随机SIS-SIRS传染病模型

doi:10.16088/j.issn.1001-6600.2025091102

摘要/Abstract

摘要： 本文研究一类同时具有SIS和SIRS传播机制的双疾病传染病模型。首先证明确定性模型4个平衡点的局部渐近稳定性,并讨论当R₁< 1且R₂< 1时无病平衡点的全局稳定性; 其次建立相应随机模型,证明随机模型全局正解的存在唯一性,给出疾病灭绝与平均持续性的充分条件,即当公式< 1时疾病灭绝,当公式> 1时疾病持久;最后通过数值模拟验证理论结果的正确性。

关键词: 双疾病, 传染病模型, 灭绝性, 持久性, Lyapunov函数

Abstract: This paper studies a class of two-disease epidemic models that incorporate both SIS and SIRS transmission mechanisms. First,the local asymptotic stability of the four local equilibrium points in the deterministic model is rigorously established,and the global stability of the disease-free equilibrium is proved under the condition that the basic reproduction numbers satisfy R₁<1 and R₂<1. Subsequently, the corresponding stochastic model is formulated,for which the existence and uniqueness of a global positive solution are proved. Furthermore,sufficient conditions for disease extinction and persistence in the mean are derived. Specifically,when the stochastic reproduction number, the disease is shown to become extinct,whereas if, the disease is persistent in the mean. Finally, theoretical results are validated through numerical simulations.

Key words: double epidemic, epidemic model, extinction, persistence in mean, Lyapunov function

中图分类号: O175.1

王展新, 韦煜明. 具有饱和发生率的确定性和随机SIS-SIRS传染病模型[J]. 广西师范大学学报（自然科学版）, 2026, 44(4): 130-146.

Wang Zhanxin, Wei Yuming. Analysis of a deterministic and stochastic SIS-SIRS epidemic model with saturated incidence rates[J]. Journal of Guangxi Normal University(Natural Science Edition), 2026, 44(4): 130-146.

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