Anticipating infectious disease emergence and documenting progress in disease elimination are important applications for the theory of critical transitions. A key problem is the development of theory relating the dynamical processes of transmission to observable phenomena. In this paper, we consider compartmental susceptibleinfectious-susceptible (SIS) and susceptible-infectiousrecovered (SIR) models that are slowly forced through a critical transition. We derive expressions for the behavior of several candidate indicators, including the autocorrelation coefficient, variance, coefficient of variation, and power spectra of SIS and SIR epidemics during the approach to emergence or elimination. We validated these expressions using individual-based simulations. We further showed that moving-window estimates of these quantities may be used for anticipating critical transitions in infectious disease systems. Although leading indicators of elimination were highly predictive, we found the approach to emergence to be much more difficult to detect. It is hoped that these results, which show the anticipation of critical transitions in infectious disease systems to be theoretically possible, may be used to guide the construction of online algorithms for processing surveillance data.

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The authors develop a multi-type branching process model of the 2014 Liberian Ebola outbreak that incorporates the impacts of changes in behavior on potential transmission scenarios, thereby informing the path to containment of the epidemic.

The frequency of opportunities for transmission is key to the severity of directly transmitted disease outbreaks in multihost communities. Transmission opportunities for generalist microparasites often arise from competitive and trophic interactions. Additionally, contact heterogeneities within and between species either hinder or promote transmission. General theory incorporating competition and contact heterogeneities for disease-diversity relationships is underdeveloped. Here, we present a formal framework to explore disease-diversity relationships for directly transmitted parasites that infect multiple host species, including influenza viruses, rabies virus, distemper viruses, and hantaviruses. We explicitly include host regulation via intra- and interspecific competition, where the latter can be dependent on or independent of interspecific contact rates (covering resource utilization overlap, habitat selection preferences, and temporal niche partitioning). We examine how these factors interact with frequency- and density-dependent transmission along with traits of the hosts in the assemblage, culminating in the derivation of a relationship describing the propensity for parasite fitness to decrease in species assemblages relative to that in single-host species. This relationship reveals that increases in biodiversity do not necessarily suppress frequency-dependent parasite transmission and that regulation of hosts via interspecific competition does not always lead to a reduction in parasite fitness. Our approach explicitly shows that species identity and ecological interactions between hosts together determine microparasite transmission outcomes in multispecies communities.

Emerging and re-emerging pathogens exhibit very complex dynamics, are hard to model and difficult to predict. Their dynamics might appear intractable. However, new statistical approaches—rooted in dynamical systems and the theory of stochastic processes—have yielded insight into the dynamics of emerging and re-emerging pathogens. We argue that these approaches may lead to new methods for predicting epidemics. This perspective views pathogen emergence and re-emergence as a “critical transition,” and uses the concept of noisy dynamic bifurcation to understand the relationship between the system observables and the distance to this transition. Because the system dynamics exhibit characteristic fluctuations in response to perturbations for a system in the vicinity of a critical point, we propose this information may be harnessed to develop early warning signals. Specifically, the motion of perturbations slows as the system approaches the transition.