广西师范大学学报（自然科学版）2026，Vol.44Issue(4)：130-146,17.DOI:10.16088/j.issn.1001-6600.2025091102
具有饱和发生率的确定性和随机SIS-SIRS传染病模型
Analysis of a deterministic and stochastic SIS-SIRS epidemic model with saturated incidence rates
摘要
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.关键词
双疾病/传染病模型/灭绝性/持久性/Lyapunov函数Key words
double epidemic/epidemic model/extinction/persistence in mean/Lyapunov function分类
数理科学引用本文复制引用
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):130-146,17.基金项目
广西自然科学基金(2023GXNSFAA026246) （2023GXNSFAA026246）
