Human mobility and disease prevalence

We examine the effect of human mobility on disease prevalence by studying the dependence of the total infected population at endemic equilibria with respect to population diffusion rates of a diffusive epidemic model. For small diffusion rates, our results indicate that the total infected population size is strictly decreasing with respect to the ratio of the diffusion rate of the infected population over that of the susceptible population. Moreover, when the disease local reproductive function is spatially heterogeneous, we found that: (i) for large diffusion rate of the infected population, the total infected population size is strictly maximized at large diffusion rate of the susceptible population when the recovery rate is spatially homogeneous, while it is strictly maximized at intermediate diffusion rate of the susceptible population when the difference of the transmission and recovery rates are spatially homogeneous; (ii) for large diffusion rate of the susceptible population, the total infected population size is strictly maximized at intermediate diffusion rate of the infected population when the recovery rate is spatially homogeneous, while it is strictly minimized at large diffusion rate of the infected population when the difference of the transmission and recovery rates is spatially homogeneous. Numerical simulations are provided to complement the theoretical results. Our studies may provide some insight into the impact of human mobility on disease outbreaks and the severity of epidemics.