具有意识影响的传染病模型分析及优化控制OA
Model Analysis and Optimal Control of an Epidemic Model with the Effects of Awareness
文章首先建立了一类具有高、低风险的易感者和有、无意识的感染者的传染病模型.其次,通过下一代矩阵法求得基本再生数,利用Hurwitz判据和LaSalle不变集原理分析了平衡点的稳定性,结合中心流形定理证明系统存在向后分岔.然后,运用庞特里亚金(Pontryagin)最大值原理研究了模型对应的优化控制问题.最后,利用数值模拟对上述理论进行了验证,同时对参数进行了灵敏度分析,讨论了参数对基本再生数的影响.结果表明,增强感染者的意识和对高危易感者接种疫苗,能够有效控制传染病的传播.
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.
王美艳;薛亚奎
中北大学 数学学院,山西 太原 030051中北大学 数学学院,山西 太原 030051
数理科学
意识计划稳定性高风险人群灵敏度分析
awareness programsstabilityhigh-risk populationsensitivity analysis
《山西大学学报（自然科学版）》 2026 (2)
244-253,10
国家自然科学基金(11301491)山西省自然科学基金(2018010221040)
评论