Inflow restrictions can prevent epidemics when contact tracing efforts are effective but have limited capacity

When a region tries to prevent an outbreak of an epidemic, like that of COVID-19, two broad strategies are initially available: limiting the inflow of infected cases using travel restrictions and quarantines, and reducing transmissions from inflowing cases using contact tracing and community interventions. A large number of papers have used epidemiological models to argue that inflow restrictions are unlikely to be effective. We conduct a mathematical analysis using a simple epidemiological model and perform simulations that show this conclusion can change if we relax the assumption of unlimited capacity in containment efforts such as contact tracing. In particular, when contact tracing is effective, but the system is close to being overwhelmed, moderate travel restrictions can have very large effects on the probability of an epidemic.