Transient indicators of tipping points in infectious diseases

Journal of the Royal Society Interface

A variety of generic indicators have been proposed to identify gradual changes in a population that can be used to anticipate the onset or conclusion of an epidemic.  Many of these indicators rely on critical slowing down, a phenomenon where a system takes a longer time to return to a stable state following a perturbation as the system approaches a tipping point. Such indicators characterize the long-term resilience of the system in the absence of any disturbances.  However, in infectious diseases systems, disturbances are frequent and direct observation of long-term resilience is rare. Thus, this work characterizes the tendency of infectious disease systems to amplify perturbations in the short term. The implication is that more frequently observed short-term behavior can provide indicators of the reducing efficacy of disease control measures prior to an epidemic or the success of control measures instituted for a widespread disease. 

In more detail, the researchers show that two measures of transient dynamics, reactivity (a measure of the potential for instantaneous growth of perturbations) and the maximum amplification (a measure of the magnitude a perturbation can attain) may be useful indicators for infectious disease systems. Using SIR models parameterized for measles and pertussis as case studies, researchers show that perturbations —  which may occur as a consequence of the roll-out of a new vaccine, for example — typically have greater growth rates and maximum size as a tipping point is approached.  This result suggests that indicators based on short-term observations of disturbances may be a useful component of forecasting systems. Such systems have important implications for health policy and may improve infectious disease preparedness efforts.

Corresponding Author: Suzanne O’Regan,

O’Regan SM, O’Dea EB, Rohani P, Drake JM. 2020 Transient indicators of tipping points in infectious diseases. J. R. Soc. Interface 17: 20200094.

Vaccine illustration by Chloe Parker