Rational social distancing in epidemics with uncertain vaccination timing

During epidemics people may reduce their social and economic activity to lower their risk of infection. Such social distancing strategies will depend on information about the course of the epidemic but also on when they expect the epidemic to end, for instance due to vaccination. Typically it is difficult to make optimal decisions, because the available information is incomplete and uncertain. Here, we show how optimal decision-making depends on information about vaccination timing in a differential game in which individual decision-making gives rise to Nash equilibria, and the arrival of the vaccine is described by a probability distribution. We predict stronger social distancing the earlier the vaccination is expected and also the more sharply peaked its probability distribution. In particular, equilibrium social distancing only meaningfully deviates from the no-vaccination equilibrium course if the vaccine is expected to arrive before the epidemic would have run its course. We demonstrate how the probability distribution of the vaccination time acts as a generalised form of discounting, with the special case of an exponential vaccination time distribution directly corresponding to regular exponential discounting.

Automated summary

During epidemics, people may decrease their social and economic activities to lower the risk of infection. The decision-making process for social distancing strategies depends on information about the epidemic course and the expected end, such as vaccination timing. Optimal decisions are challenging due to incomplete and uncertain information. In this study, we demonstrate how optimal decision-making is influenced by information about vaccination timing in a differential game that considers individual decision-making and a probability distribution for vaccine arrival. We predict that social distancing will be stronger when vaccination is expected earlier and when the probability distribution is more sharply peaked. Equilibrium social distancing significantly deviates from the no-vaccination equilibrium only if the vaccine is expected to arrive before the epidemic would naturally end. We show how the probability distribution of vaccination time acts as a generalized form of discounting, with exponential vaccination time distribution corresponding to regular exponential discounting.