Controlling Epidemics via Testing

In this paper, we focus on the effect that testing centers (which detect and quarantine infected individuals) have on mitigating the evolution of an epidemic. We incorporate diffusion-style mobility of infected but undetected individuals, as opposed to detected and quarantined ones. We compute the total and maximum (over time) spatially averaged density of infected individuals (detected or not), which are useful metrics of the epidemic's impact on a population, as functions of the testing center spatial density. Even under conditions where the epidemic has the natural potential to spread, we find that a 'phase transition' occurs as the testing center spatial density increases. For any testing density above a certain threshold the epidemic is suppressed and dies out, while below it propagates and evolves naturally albeit still strongly depending on the testing center density. This analysis further allows to optimize the testing certain density so that the epidemic's evolution does not inundate or exhaust critical health care resources, like ICU bed capacity.