Asymptotic Distribution Of A Two-strain Malaria Transmission Model With Spatial Heterogeneity And Vector Bias

A two-strain reaction-diffusion malaria epidemic model which contains spatial heterogeneity and vector bias is designed in this paper.The interaction between sensitive and resistant strains was characterized by threshold dynamics analysis.Firstly,we define the basic reproduction number Ri(i=1,2)and the invasion reproduction number(?)of the single strain,the qualitative relationship between the corresponding local reproduction number and local invasion regeneration number is also studied.Secondly,the influence of diffusion coefficient and spatial heterogeneity on Ri and(?)are analyzed,in other words,we give the calculation formula of Ri and(?)when diffusion coefficient tends to zero or tends to infinity.Finally,through qualitative analysis,we obtain that when Ri<1(i=1,2),the disease-free equilibrium is globally stable while competitive exclusion is a possible outcome when Ri>1>Rj(i?j,i,j=1,2),in addition,it is possible for two strains to coexist if Ri>1,(?)>1.