考虑疫苗接种和失效的疟疾传播动力学建模与分析  

Modeling and Analysis of Malaria Transmission Dynamics Considering Vaccination and Vaccine Failure

作　　者：郭松柏 薛玉玲 何敏 崔景安 GUO SONGBAI;XUE YULING;HE MIN;CUI JING-AN(School of Science,Beijing University of Civil Engineering and Architecture,Beijing 102616,China)

机构地区：[1]北京建筑大学理学院,北京102616

出　　处：《应用数学学报》2024年第1期1-11,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11901027,12171003);中国博士后科学基金(2021M703426);北京建筑大学建大英才项目(JDYC20200327);北京建筑大学研究生创新项目(PG2022143)资助。

摘　　要：针对疟疾疫苗在疟疾传播方面的实际问题,构建了一个具有疫苗接种和失效的疟疾传播动力学模型,并计算了该模型的控制再生数Rc.给出了该模型的无疟疾平衡点和疟疾平衡点关于R。的存在性条件.利用Lyapunov函数法结合广义的Lyapunov-LaSalle定理,建立了无疟疾平衡点和疟疾平衡点关于Rc的全局渐近稳定的充分必要条件.In view of the practical problems of malaria vaccine in malaria transmission,a dynamical model of malaria with vaccination and vaccine failure is constructed,and the control reproduction number R_c is calculated.The existence conditions of malaria-free and malaria equilibria in terms of R_c are given.By using the Lyapunov function method and the generalized Lyapunov-Lasalle theorem,the sufficient and necessary conditions for the global asymptotic stability of malaria-free and malaria equilibria with respect to R_c are established.

关 键 词：疟疾 动力学模型 控制再生数 全局稳定性 

分 类 号：O175.13[理学—数学]