山西大学学报（自然科学版）2025，Vol.48Issue(6)：1103-1112,10.DOI:10.13451/j.sxu.ns.2025079
一类具有非线性发生率的随机SIR模型的Melnikov混沌
Melnikov Analysis of Chaos in a Stochastic SIR Model with Nonlinear Incidence Rate
摘要
Abstract
In view of the fact that the prevalence of diseases is often disturbed by random factors,this paper studies the chaotic dy-namics of a class of SIR model with nonlinear incidence rate through the infection rate disturbed by bounded noise.Based on the homoclinic bifurcation and by using the stochastic Melnikov theory,from the perspective of mathematical theory,the sufficient condition for the possible occurrence of chaos in the model is derived,and the threshold of chaos in the model under bounded noise disturbance is obtained.Moreover,the influence of the noise amplitude on the chaotic dynamic behavior of the SIR model is elucidated.Numerical simulations,including potential,threshold curve graphs,and phase portraits,are used to verify the results of the theoretical analysis.The research results contribute to accurately predicting the disease transmission trends,provide theoretical support for formulating public health prevention and control strategies,and facilitate the scientific prevention and control of epi-demics.关键词
非线性发生率/Melnikov理论/混沌/同宿分岔Key words
nonlinear incidence rate/Melnikov theorem/chaos/homoclinic bifurcation分类
数学引用本文复制引用
石艳香..一类具有非线性发生率的随机SIR模型的Melnikov混沌[J].山西大学学报（自然科学版）,2025,48(6):1103-1112,10.基金项目
国家自然科学基金(12571537) （12571537）
山西省自然科学基金(201901D111041 （）
201601D202002) （）
