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 \({\hat{R}}_{i}\) 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 \(R_{i}>1>R_{j}\) \((i\ne j, i,j=1,2)\), and a unique solution with two strains coexist to the model is globally asymptotically stable if \(R_{i}>1\), \({\hat{R}}_{i}>1\). 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.

在本文中，我们介绍了一种反应扩散疟疾模型，该模型结合了矢量偏倚，空间异质性，敏感和耐药菌株。我们研究的主要问题是模型的阈值动力学，特别是空间结构的存在是否会允许两个应变共存。为了实现这一目标，我们定义了基本再生数\（R_ {I} \）并引入入侵再生数\（{\帽子{R}} _ {I} \）应变\（I（I = 1,2）\）。定量分析表明，如果\（R_ {i} <1 \），则无病稳态是全局渐近稳定的，而竞争排斥则是菌株i持续存在且菌株j持续存在当（（R_ {i}> 1> R_ {j} \） \（（i \ ne j，i，j = 1,2）\）和具有两个应变的唯一解共存时可能消失如果\（R_ {i}> 1 \），\（{\ hat {R}} _ {i}> 1 \），则模型的全局渐近稳定。数值模拟加强了这些分析结果，并证明了两种菌株之间的流行病学相互作用，讨论了抗药性菌株的影响，并研究了矢量偏置对疟疾传播的影响。