一类具有交错扩散项的疟疾模型的共存解

Coexistence solutions for a class of malaria models with cross-diffusion terms

为了解疟疾在人群和蚊群中的传播机制,在传统的疟疾常微分方程模型中引入了较为复杂的扩散结构和异质环境,探讨了基本再生数与交错扩散系数及其他参数的关系,利用上下解方法研究了共存解的存在性.结果表明,当低风险阈值大于1时,人群和蚊群携带的疟疾病毒将会共存,不利于疟疾的防控;当高风险阈值小于或等于1时,则疟疾病毒就会消失.给出了数值模拟及流行病学解释.

In order to understand the transmission mechanism of malaria in human and mosquitoes,complex diffusion structures and heterogeneous environments is introduced to traditional malaria ordinary differential equation models.The relationship between the basic reproduction number and the cross-diffusion coefficient as well as other parameters is explored,and the upper-lower solution method is also utilized to study the existence of coexisting solutions.The results imply that when the low-risk threshold value is greater than one,the malaria virus carried by populations and mosquito populations can coexist,which is not conducive to the prevention and control of malaria.While the high-risk threshold value is less than or equal to one,the malaria virus will disappear.Finally,numerical simulations and epidemiological explanations are provided.