Public control of rational and unpredictable epidemics

Efforts to improve disease forecasting are often justified on the grounds that accurate and reliable forecasts offer opportunities to improve response to epidemics. Yet little is known about how disease forecasts influence the responsiveness to public health interventions. This paper couples an optimal stopping model and rational disease prevention with a stochastic compartmental epidemiological model of disease spread to develop a framework for evaluating the timing of public health interventions in response to rational but unpredictable epidemics. Optimal behavior by a public health agency is characterized by a pair of critical prevalence thresholds that trigger implementation and suspension of a public prevention program. Unlike existing economic thresholds for disease prevention, our decision thresholds account for time-varying probabilities of different levels of infection, prevention by private individuals, and the likelihood of crossing epidemiological thresholds that determine disease persistence.