Analysis of a two-strain malaria transmission model with spatial heterogeneity and vector-bias

In this paper, we introduce a reaction–diffusion malaria model which incorporates vector-bias, spatial heterogeneity, sensitive and resistant strains. The main question that we study is the threshold dynamics of the model, in particular, whether the existence of spatial structure would allow two strains to coexist. In order to achieve this goal, we define the basic reproduction number R_i and introduce the invasion reproduction number R̂_i for strain i (i=1,2) . A quantitative analysis shows that if R_i<1 , then disease-free steady state is globally asymptotically stable, while competitive exclusion, where strain i persists and strain j dies out, is a possible outcome when R_i>1>R_j (i j, i,j=1,2) , and a unique solution with two strains coexist to the model is globally asymptotically stable if R_i>1 , R̂_i>1 . Numerical simulations reinforce these analytical results and demonstrate epidemiological interaction between two strains, discuss the influence of resistant strains and study the effects of vector-bias on the transmission of malaria.