Rational social distancing policy during epidemics with limited healthcare capacity

Epidemics of infectious diseases posing a serious risk to human health have occurred throughout history. During recent epidemics there has been much debate about policy, including how and when to impose restrictions on behaviour. Policymakers must balance a complex spectrum of objectives, suggesting a need for quantitative tools. Whether health services might be ‘overwhelmed’ has emerged as a key consideration. Here we show how costly interventions, such as taxes or subsidies on behaviour, can be used to exactly align individuals’ decision making with government preferences even when these are not aligned. In order to achieve this, we develop a nested optimisation algorithm of both the government intervention strategy and the resulting equilibrium behaviour of individuals. We focus on a situation in which the capacity of the healthcare system to treat patients is limited and identify conditions under which the disease dynamics respect the capacity limit. We find an extremely sharp drop in peak infections at a critical maximum infection cost in the government’s objective function. This is in marked contrast to the gradual reduction of infections if individuals make decisions without government intervention. We find optimal interventions vary less strongly in time when interventions are costly to the government and that the critical cost of the policy switch depends on how costly interventions are.Author summary: The question of how to determine policies during epidemics is a subject of broad contemporary interest. How and when should society impose behavioural restrictions in order to reduce infections? Policymakers have to balance many objectives, suggesting a need for quantitative tools for designing optimal intervention policy. Previous work on optimal policy-making typically sidesteps the question of how the population follows any intervention chosen by a government. Furthermore, the cost of implementing an intervention is also usually ignored. Our work overcomes these shortcomings. We analyse how the population chooses behaviour in a self-organised way. This can be influenced by the government so as to optimise its own objective function. Its objectives can be different from the individuals. Our work represents a proof-of-principle that costly policy interventions can be developed in the environment of (i) a disease with well-understood epidemiological character (ii) health-care capacity limits (iii) where those interventions are costly to implement. For these reasons we believe it highlights an opportunity to develop deployable policymaking tools and further advances our understanding of epidemiology when individuals adapt their behaviour in response to perceived dangers.