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