A diffusive virus model with a fixed intracellular delay and combined drug treatments

The method of administration of an effective drug treatment to eradicate viruses within a host is an important issue in studying viral dynamics. Overuse of a drug can lead to deleterious side effects, and overestimating the efficacy of a drug can result in failure to treat infection. In this study, we proposed a reaction-diffusion within-host virus model which incorporated information regarding spatial heterogeneity, drug treatment, and the intracellular delay to produce productively infected cells and viruses. We also calculated the basic reproduction number R under the assumptions of spatial heterogeneity. We have shown that the infection-free periodic solution is globally asymptotically stable when R< 1 , whereas when R> 1 there is an infected periodic solution and the infection is uniformly persistent. By conducting numerical simulations, we also revealed the effects of various parameters on the value of R. First, we showed that the dependence of R on the intracellular delay could be monotone or non-monotone, depending on the death rate of infected cells in the immature stage. Second, we found that the mobility of infected cells or virions could facilitate the virus clearance. Third, we found that the spatial fragmentation of the virus environment enhanced viral infection. Finally, we showed that the combination of spatial heterogeneity and different sets of diffusion rates resulted in complicated viral dynamic outcomes.