On Robust Economic Control of Epidemics with Application to COVID-19

As of September 2021 the ongoing COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), had already resulted in more than two hundred million cases infected and five million deaths worldwide. It is also causing tremendous economic losses to many nations. Governments in many countries are striving to salvage their economies. In this paper, we propose a new robust economic epidemic control problem that minimizes the worst medical/preventive costs under some epidemic control constraints. A simple SIRD-based epidemiology model with two uncertainties: The uncertain rate of infected cases which are undetected or asymptomatic and the uncertain effectiveness rate of control, is considered. With a linear control policy, we show sufficient conditions for the epidemic that is deemed to be “well-controlled" in the sense that infected cases go down to zero asymptotically and are upper bounded uniformly. Then we establish that the optimal linear policy that minimizes the medical/preventative costs. Finally, we also provide some numerical studies using the historical COVID-19 contagion data in Taiwan. A comparison with and without lockdown considerations is also provided.