Controlling epidemic extinction using early warning signals

As the recent COVID-19 pandemic has shown us, there is a critical need to develop new approaches to monitoring the outbreak and spread of infectious disease. Improvements in monitoring will enable a timely implementation of control measures, including vaccine and quarantine, to stem the spread of disease. One such approach involves the use of early warning signals to detect when critical transitions are about to occur. Although the early detection of a stochastic transition is difficult to predict using the generic indicators of early warning signals theory, the changes detected by the indicators do tell us that some type of transition is taking place. This observation will serve as the foundation of the method described in the article. We consider a susceptible–infectious–susceptible epidemic model with reproduction number R0>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0>1$$\end{document} so that the deterministic endemic equilibrium is stable. Stochastically, realizations will fluctuate around this equilibrium for a very long time until, as a rare event, the noise will induce a transition from the endemic state to the extinct state. In this article, we describe how metric-based indicators from early warning signals theory can be used to monitor the state of the system. By measuring the autocorrelation, return rate, skewness, and variance of the time series, it is possible to determine when the system is in a weakened state. By applying a control that emulates vaccine/quarantine when the system is in this weakened state, we can cause the disease to go extinct earlier than it otherwise would without control. We also demonstrate that applying a control at the wrong time (when the system is in a non-weakened, highly resilient state) can lead to a longer extinction time than if no control had been applied. This feature underlines the importance of determining the system’s state of resilience before attempting to affect its behavior through control measures.