高师理科学刊2025，Vol.45Issue(7)：17-23,7.DOI:10.3969/j.issn.1007-9831.2025.07.005
具有饱和出生函数和时滞的阶段结构传染病模型稳定性分析
Stability analysis of a stage-structured epidemic model with saturation birth function and delay
摘要
Abstract
In a class of stage-structured epidemic models with saturated birth functions,the scenario where the disease spreads only among adult individuals and severely affects their reproductive capacity was considered,the time delay of virus replication was introduced.Based on the basic reproduction number for population survival and the basic reproduction number for disease transmission,the existence of equilibrium points in the model was determined using dynamical analysis methods,the stability of these equilibrium points was then analyzed.The results indicated that when the basic reproduction number for population survival was no greater than one,the population would go extinct;when the basic reproduction number for population survival exceeded one,while the basic reproduction number for disease transmission was no greater than one,the disease-free equilibrium point for population survival was always locally asymptotically stable for all delay values;when the basic reproduction number for disease transmission exceeded one,if the delay sufficiently small,the endemic equilibrium point for population survival was locally asymptotically stable,as the delay increased,the stability of the equilibrium point was lost,and a Hopf bifurcation emerged.Numerical simulations were conducted to validate the analytical results.关键词
阶段性结构/传染病模型/平衡点/稳定性/Hopf分支Key words
stage structure/epidemic model/equilibrium/stability/Hopf bifurcation分类
数理科学引用本文复制引用
于莉琦,贺树立..具有饱和出生函数和时滞的阶段结构传染病模型稳定性分析[J].高师理科学刊,2025,45(7):17-23,7.基金项目
黑龙江省自然科学基金项目(LH2022A022) （LH2022A022）
