Control Of Epidemic Spreads Via Testing And Lock-Down

Testing and lock-down provide two important control levers to combat the spread of an infectious disease. Testing is a targeted instrument that permits the isolation of infectious individuals. Lock-down, on the other hand, is blunt and restricts the mobility of all people. In this paper, we present a compartmental epidemic model that accounts for the impact of lockdown and different kinds of testing, motivated by the nature of the ongoing COVID-19 outbreak. We consider the testing of symptomatic, contact traced and randomly chosen asymptomatic populations. Using the model, we characterize static mobility levels and testing requirements that can mitigate the disease spread asymptotically. We then use the model to establish that an optimal dynamic lock-down and random testing sequence, that minimizes a detailed cost of the epidemic over a finite horizon, is extremal. The optimal sequence of actions is hard to compute. We thus provide two computationally lightweight dynamic control strategies that use extremal actions and compare them numerically with those that are static.