山西大学学报（自然科学版）2026，Vol.49Issue(2)：244-253,10.DOI:10.13451/j.sxu.ns.2024024
具有意识影响的传染病模型分析及优化控制
Model Analysis and Optimal Control of an Epidemic Model with the Effects of Awareness
摘要
Abstract
This paper first establishes a class of infectious disease model with high and low risk susceptible persons and infected per-sons who are unconscious.Secondly,the basic regeneration number is obtained by the next generation matrix method,the stability of the equilibrium point is analyzed by Hurwitz criterion and LaSalle invariant set principle,and the backward bifurcation is proved by the central prevalence theorem.Then,the optimal control problem corresponding to the model is studied using the Pontryagin maxi-mum principle.Finally,the above theory is verified by numerical simulation,and the sensitivity analysis of parameters is carried out,and the influence of parameters on the basic regeneration number is discussed.The results showed that enhancing the awareness of infected people and vaccinating high-risk susceptible people could effectively control the spread of infectious diseases.关键词
意识计划/稳定性/高风险人群/灵敏度分析Key words
awareness programs/stability/high-risk population/sensitivity analysis分类
数理科学引用本文复制引用
王美艳,薛亚奎..具有意识影响的传染病模型分析及优化控制[J].山西大学学报（自然科学版）,2026,49(2):244-253,10.基金项目
国家自然科学基金(11301491) （11301491）
山西省自然科学基金(2018010221040) （2018010221040）
