Dynamics of a multi-strain malaria model with diffusion in a periodic environment.

This paper mainly explores the complex impacts of spatial heterogeneity, vector-bias effect, multiple strains, temperature-dependent extrinsic incubation period (EIP) and seasonality on malaria transmission. We propose a multi-strain malaria transmission model with diffusion and periodic delays and define the reproduction numbers $R_i$ and ${\hat{R}}_i$ (i = 1, 2). Quantitative analysis indicates that the disease-free ω-periodic solution is globally attractive when $R_i<1$, while if $R_i>1>R_j$ ($i\ne j,i,j=1,2$), then strain i persists and strain j dies out. More interestingly, when $R_1$ and $R_2$ are greater than 1, the competitive exclusion of the two strains also occurs. Additionally, in a heterogeneous environment, the coexistence conditions of the two strains are ${\hat{R}}_1>1$ and ${\hat{R}}_2>1$. Numerical simulations verify the analytical results and reveal that ignoring vector-bias effect or seasonality when studying malaria transmission will underestimate the risk of disease transmission.