On the management of population immunity.

This paper considers a susceptible-infected-recovered type model of infectious diseases, such as COVID-19 or swine flu, in which costly treatment or vaccination confers immunity on recovered individuals. Once immune, individuals indirectly protect the remaining susceptibles, who benefit from a measure of herd immunity. Treatment and vaccination directly induce such herd immunity, which builds up over time. Optimal treatment is shown to involve intervention at early stages of the epidemic, while optimal vaccination may defer intervention to intermediate stages. Thus, while treatment and vaccination have superficial similarities, their effects and desirability at different stages of the epidemic are different. Equilibrium vaccination is qualitatively similar to socially optimal vaccination, while equilibrium treatment differs in nature from socially optimal treatment. The optimal policies are compared to traditional non-economic public health interventions which rely on herd immunity thresholds.

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. 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.