Odum School of Ecology
University of Georgia
Early warning signals of critical transitions in infectious disease dynamics
Predicting abrupt shifts in state ('critical transitions') of complex systems is a key research topic in a variety of scientific and social domains. Mechanisms for abrupt shifts include environmental shocks, strong stochasticity, and small changes in underlying drivers whereby the system crosses a 'tipping point'. In the latter case, where the change in the external variable is slow relative to the characteristic speed of the internal variables, the tipping point may be described mathematically as a bifurcation. This class of critical transition may be predictable because prior to reaching the dynamical threshold, the system may exhibit 'critical slowing down’. Statistical signatures of critical slowing down have been detected from temporal and spatial data in a wide range of biological systems, including the global climate system, ecosystems, experimental microcosms and physiological systems.
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 talk, we consider compartmental epidemiological SIS and SIR models that are slowly forced through a critical transition. We derived 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 showed that moving-window estimates of the candidate indicators 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.
Sponsored by the Department of Mathematical Sciences
Host: Dmitry Rachinskiy
Refreshments will be served in FO 2.610F 30 minutes before the talk begins.