A two-strain malaria transmission model with seasonality and incubation period

Malaria is one of the most common mosquito-borne diseases in the world. To understand the joint effects of the vector-bias, seasonality, spatial heterogeneity multi-strain and the extrinsic incubation period of the parasite on the dynamics of malaria, we formulate a time-periodic two-strain malaria reaction-diffusion model with delay and nonlocal terms. We then consider threshold conditions that determine whether malaria will spread. More specifically, the basic reproduction number R-i for single strain-i and invasion numberR(i) for each strain-i(i=1,2) are derived. Our results imply that ifmax{R-1,R-2}<1, then the disease-free periodic solution is globally attractive; if R-i>1>R-j(i, j=1,2,i not equal j), then competitive exclusion, where the jth strain dies out and the ith strain persists; if min{R-1,R-2,R-1,R-2}>1, then the disease persists. Our numerical simulations show that spatially heterogeneous infection can increase the basic reproduction number and the omission of the vector-bias effect will underestimate the infection risk of the disease.