Modeling the coupling between a COVID-19-like epidemic and the economy

Abstract

We consider a compartmental model adapted to the case of COVID-19 that takes into account the detection of ill individuals and the cost of medical treatment and investigate the effect of a budget constraint. Our analysis shows how the collapse of the budget can drastically change the outcome of an epidemics. We see how with a good testing policy the epidemic might be controllable. By introducing a lockdown period, we show that the final number of deaths can be reduced substantially and observe that a budget collapse introduces rather extreme effects. We find that there exists a well-defined optimal starting point for a lockdown. We also looked at the consequences of a loss of immunity and found that then a budget collapse can occur for smaller costs of medical treatment.