A cost-benefit analysis of the COVID-19 disease

The British government has been debating how to escape from the lockdown without provoking a resurgence of the COVID-19 disease. There is a growing recognition of the damage the lockdown has caused to economic and social life. This paper presents a simple cost-benefit analysis inspired by optimal control theory and incorporating the SIR model of disease propagation. It also reports simulations informed by the theoretical discussion. The optimal path for government intervention is computed under a variety of conditions. These include a cap on the permitted level of infection to avoid overload of the health system, and the introduction of a test and trace system. We quantify the benefits of early intervention to control the disease. We also examine how the government's valuation of life influences the optimal path. A 10-week lockdown is only optimal if the value of life for COVID-19 victims exceeds 10m pound. The study is based on a standard but simple epidemiological model, and should therefore be regarded as presenting a methodological framework rather than giving policy prescriptions.