On the effect of lowering population's movement to control the spread of an infectious disease

Abstract

We study the asymptotic behavior of endemic equilibrium solutions of a diffusive epidemic model in spatially heterogeneous environment when the diffusion rates dS of the susceptible and dI of the infected groups approach zero. Our results indicate that when dI and dS are sufficiently small, the size of dIdS plays a crucial role in the dynamics of the disease in the sense that: (i) if dIdS is small, the disease may persist and the total size of the infected group will be maximized; (ii) if dIdS is large, then the total size of the susceptible group is maximized while the total size of the infected group is minimized. Hence, our results suggest that lowering the movement rate of the population in an attempt to limit infection is an effective control strategy if the susceptible hosts' movement rate is kept sufficiently smaller than that of the infected individuals.