Evolution dynamics of a time-delayed reaction–diffusion HIV latent infection model with two strains and periodic therapies

Abstract

Multiple HIV stains coinfection within the host has always been a challenging problem in clinical treatment and mathematical modeling. In order to explore joint effects of spatial factors, latent infection, latent period, and periodic therapies on the dynamics of HIV infection, we formulate a time-periodic reaction diffusion HIV latent infection model with multiple strains, four latent periods, and spatial heterogeneity. Applying the next infection operator, we derive the basic reproduction number Ri0 and the invasion number R˜i0(i=1,2), which is shown to be the threshold parameter determining the capability of the ith strain invading the jth strain (i≠j,i,j=1,2), thereby affecting the competitive evolution result of the two HIV stains. More precisely, the infection-free steady state is globally attractive when Ri0 both less than unity; if Ri0 larger than unity and Rj0 less than unity (i≠j), then the ith strain outcompetes the jth strain, i.e., the ith strain persists and the jth stain will extinct eventually; if R˜i0>1(i=1,2), then the infection is uniformly persistent within the host. Numerical simulations are conducted to verify these analytical results.