Rational policy design for epidemics

We study the optimal control of an epidemic by governments and individuals using a Hamiltonian approach. Assuming that government and individuals optimise (potentially different) value functions, we show how subsidies and taxes can be used by governments to exactly align individuals’ decision making with government preferences. To capture the limited capacity of the health care system we include a term that increases sharply when the fraction of infected exceeds a threshold. 

In addition, we study a previously unexplored situation in which the government pays the cost of subsidising individual behaviour. We find that this can substantially affect the optimal trajectories.

The epidemic is modelled with a standard SIR compartmentalised model in which the population consists of Susceptible, Infected and Recovered categories between which individuals transition over time. Social activity of the population influences the infection incidence. We parametrise the population’s preferences via the costs of (i) being infected and (ii) the cost of reducing social and economic activity. Self-organised social distancing will arise as a (Nash) equilibrium when the cost to being infected outweighs the cost associated with the reduction of social activity.