Patch model for border reopening and control to prevent new outbreaks of COVID-19.

In this paper, we propose a two-patch model with border control to investigate the effect of border control measures and local non-pharmacological interventions (NPIs) on the transmission of COVID-19. The basic reproduction number of the model is calculated, and the existence and stability of the boundary equilibria and the existence of the coexistence equilibrium of the model are obtained. Through numerical simulation, when there are no unquarantined virus carriers in the patch-2, it can be concluded that the reopening of the border with strict border control measures to allow people in patch-1 to move into patch-2 will not lead to disease outbreaks. Also, when there are unquarantined virus carriers in patch-2 (or lax border control causes people carrying the virus to flow into patch-2), the border control is more strict, and the slower the growth of number of new infectious in patch-2, but the strength of border control does not affect the final state of the disease, which is still dependent on local NPIs. Finally, when the border reopens during an outbreak of disease in patch-2, then a second outbreak will happen.