一类空间异质环境中疟疾周期模型的传播动力学  

The Transmission Dynamics of Malaria Periodic Model in Spatially Heterogeneous Environment

作　　者：宋小飞 朱敏 刘梦丽 SONG XIAOFEI;ZHU MIN;LIU MENGLI(School of Mathematics and Statistics,Anhui Normal University,Wuhu 241000,China)

机构地区：[1]安徽师范大学数学与统计学院,芜湖241000

出　　处：《应用数学学报》2022年第6期873-888,共16页Acta Mathematicae Applicatae Sinica

基　　金：家自然科学基金(No.11801009);安徽省自然科学基金(No.2208085MA08)资助项目。

摘　　要：季节的更替和环境的差异会导致疾传播具有时间周期性和空间异质性的特点。我们在本文将这两个特征共同引入到疮疾模型中,并研究了其传播动力学.基于下一代感染算子和相关的特征值理论,我们探讨出症疾模型的基本再生数R_(0)^(T)与时间周期性及空间异质性的关联性。利用阈值R_(0)^(T),进一步证明了当R_(0)^(T)<1时,一定条件下无病平衡点是全局渐近稳定的,以及当R_(0)^(T)>1时,模型的稳态周期解是存在唯一且全局稳定的.通过理论分析和数值模拟表明,疟疾传播最终将呈现周期性,并且在异质环境中的传播也更复杂。Seasonal changes and environmental differences can lead to the time-periodic and space-heterogeneous characteristics of malaria transmission.In this paper,we introduce these two characteristics together into the malaria model and study its transmission dynamics.Based on the next generation infection operator and the associated eigenvalue theory,we explore the relationship between the basic reproduction number R_(0)^(T) and temporal periodicity as well as spatial heterogeneity in the malaria model.Using the threshold R_(0)^(T),we further prove that when R_(0)^(T)<1,the disease-free equilibrium point is globally asymptotically stable under certain conditions,and while R_(0)^(T)>1,the steady-state periodic solution of the model is unique and globally stable.Theoretical analysis and numerical simulations show that malaria transmission eventually presents periodicity,and will be more complex in heterogeneous environments.

关 键 词：疟疾模型 周期性 异质性 基本再生数 

分 类 号：O29[理学—应用数学]