The vector-host epidemic model with multiple strains in a patchy environment

Abstract Spatial heterogeneity plays an important role in the distribution and persistence of infectious diseases. In this article, a vector-host epidemic model is proposed to explore the effect of spatial heterogeneity on the evolution of vector-borne diseases. The model is a Ross-McDonald type model with multiple competing strains on a number of patches connected by host migration. The multi-patch basic reproduction numbers Rj0, j = 1, 2, · · · , l are respectively derived for the model with l strains on n discrete patches. Analytical results show that if Rj0 < 1, then strain j cannot invade the patchy environment and dies out. The invasion reproduction numbers R i , i, j = 1, 2, i 6= j are also derived for the model with two strains on n discrete patches. It is shown that the invasion reproduction numbers R i , i, j = 1, 2, i 6= j provide threshold conditions that determine the competitive outcomes for the two strains. Under the condition that both invasion reproduction numbers are lager than one, the coexistence of two competing strains is rigorously proved. However, the two competing strains cannot coexist for the corresponding model with no host migration. This implies that host migration can lead to the coexistence of two competing strains and enhancement of pathogen genetic diversity. Global dynamics is determined for the model with two competing strains on two patches. The results are based on the theory of type-K monotone dynamical systems.