Abstract
As we strive towards the elimination of many burdensome diseases, the question of when intervention efforts may cease is increasingly important. It can be very difficult to know when prevalences are low enough that the disease will die out without further intervention, particularly for diseases that lack accurate tests. The consequences of stopping an intervention prematurely can put back elimination efforts by decades.Critical slowing down theory predicts that as a dynamical system moves through a critical transition, deviations from the steady state return increasingly slowly. We study two potential indicators of disease elimination predicted by this theory, and investigate their response using a simple stochastic model. We compare our dynamical predictions to simulations of the fluctuation variance and coefficient of variation as the system moves through the transition to elimination. These comparisons demonstrate that the primary challenge facing the analysis of early warning signs in timeseries data is that of accurately ‘detrending’ the signal, in order to preserve the statistical properties of the fluctuations. We show here that detrending using the mean of even just four realisations of the process can give a significant improvement when compared to using a moving window average.Taking this idea further, we consider a ‘metapopulation’ model of an endemic disease, in which infection spreads in various separated areas with some movement between the subpopulations. We successfully predict the behaviour of both variance and the coefficient of variation in a metapopulation by using information from the other subpopulations to detrend the system.
Highlights
The battle against infectious diseases includes some notable success stories, including the global eradication of smallpox (Fenner, 1982) and wild poliovirus type 2 (Adams and Salisbury, 2015), while the global mortality rate for malaria fell by 60% between 2000 and 2015 (The World Health Organisation, 2015)
Each elimination program shares one fundamental challenge: how do we know when we can relax control? In this paper, we propose the use of statistical indicators derived using the theory of critical slowing down to assess how close the system is to eradication
The purple line is the analytical prediction obtained by numerically solving Eq (10); the green line is the steady state variance obtained by Please cite this article as: A
Summary
The battle against infectious diseases includes some notable success stories, including the global eradication of smallpox (Fenner, 1982) and wild poliovirus type 2 (Adams and Salisbury, 2015), while the global mortality rate for malaria fell by 60% between 2000 and 2015 (The World Health Organisation, 2015). The 2012 London Declaration on neglected tropical diseases (NTDs) built on these successes by establishing goals for elimination and eradication of 10 NTDs by 2020. The intention of this declaration is to achieve elimination through various active interventions, from vector control to mass drug administration. The theory of critical slowing down observes that in a dynamical system close to a critical transition, the rate of recovery from perturbations reduces. This is because as a steady state changes stability the real part of the dominant eigenvalue must pass through zero. Since real world systems are subject to noise, this phenomenon can be detected indirectly from an increasing “memory” in stochastic fluctuations, resulting in changes in statistical indicators (or early warning signs, EWS) such as variance and autocorrelation (Scheffer et al, 2009)
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