Impact of Travel Between Patches for Spatial Spread of Disease

A patch model is proposed to study the impact of travel on the spatial spread of disease between patches. The basic reproduction number for the i-th patch in isolation, is obtained along with the basic reproduction number of the system, $mathcal{R}_0$. Inequalities describing the relationship between these numbers are also given. For a two-patch model with one high prevalence patch and one low prevalence patch, results pertaining to the dependence of $mathcal{R}_0$ on the travel rates between the two patches are obtained. For parameters relevant for influenza, the effects of travel restrictions are also discussed. Results show that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease.