一类具变系数交错扩散的登革热模型  

A Dengue Fever Model Incorporating Heterogeneous Cross-Diffusion

作　　者：朱敏 刘梦丽 Min Zhu;Mengli Liu(School of Mathematics and Statistics,Anhui Normal University,Anhui Wuhu 241000)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241000

出　　处：《数学物理学报（A辑）》2022年第1期201-215,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(11801009);安徽师范大学科研启动基金(751993)。

摘　　要：该文在登革热的传播模型中引入较复杂的异质性交错扩散,用于描述人群和蚊群的相互扩散现象,并探讨交错扩散对模型动力学的影响,以及根据风险阈值对稳态共存解存在性进行分析.结果表明,风险阈值不仅与交错扩散有关,而且直接影响着模型的动力学,如果风险阈值大于1,并伴随其它条件成立,则人群和蚊群携带的病毒会共存,不利于登革热的控制.最后给出一些传染病学及模型动力学解释.To describe the mutual diffusion phenomenon between human and mosquitoes in the spread and control of dengue fever,we introduce more complex heterogeneous cross-diffusion into the dengue fever model,and explore the impact of cross-diffusion on its dynamics.In view of the contagion risk threshold,we are devoted to analyzing the existence and non-existence of coexistence solution for the steady state.The findings show that if the contagion risk threshold is greater than one associated with some conditions,this scenario is disadvantage to the control of dengue fever,as it will lead to the coexistence of the viruses carried by human and by mosquitoes.Some epidemiological explanations are presented finally.

关 键 词：登革热模型 异质性交错扩散 共存解 传染风险阈值 

分 类 号：O175.21[理学—数学]