A cost–benefit analysis of the COVID-19 disease

Abstract

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.

Balancing costs and benefits of pandemic control in an outbreak phase

“…Our functional form of C(R t ) itself is different fromĈ(q), while the following basic assumptions, Eqs. (1,2,3,4), are essentially the same as Rowthorn 2) . Hereafter, we refer to the social cost per unit time as 'intervention cost' in the form of C(R t ).…”

“…R N equals the basic reproduction number 13) R 0 for the initial phase of infection. These measures have a negative influence on the economy and society 2) . This social cost,Ĉ, is positively correlated to the strength of the measure.…”

“…, where q represents the intensity of social intervention against pandemics. Then, he defined the social cost per unit of time as a function of q:Ĉ =Ĉ(q) 2,4) . He assumed C(0) = 0 because there is no infection control at q = 0.…”

“…These results were obtained using numerical simulation because Rowthorn assumed that explicit solution was unavailable in this issue 2) . While the methodology and results of this study 2,4) are pioneering and significant, they are not straightforward enough to generalise their results because the study investigated specific situations with given parameter sets. Therefore, explicit solutions independent of specific parameters are needed to reveal the universal property.…”

“…From a Physics perspective, the optimisation in CBA is similar to finding the minimum state of energy. In addition, the finding 2,4) that the most efficient process includes the stationary state suggests an analogous structure with thermodynamic irreversibility.…”