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…
Second order statistics such as variance and autocorrelation can in principle provide early warning of disease (re-)emergence. Such statistics can detect the approach to an…
The prevalence of a pathogen emerging in a population varies in a complex manner that is difficult to model and predict, due in part to…
Ecological systems sometimes change abruptly to a much different states. For example, a clear lake may rapidly become turbid and green due to the growth…
Bifurcation delay is a phenomenon that occurs when dynamical systems go through a critical transition. Bifurcation delay occurs because the state of the system may…
The elimination of malaria and other mosquito-borne pathogens is a major public health issue worldwide. A considerable obstacle to disease elimination in resource poor countries…
Early warning signals of critical transitions arise due to critical slowing down as a dynamical system approaches a tipping point. Extinction of a biological population…
Early warning signals for critical transitions have now been described from a number of ecological and geophysical systems. Most of these signals reflect a dynamical…
Emerging pathogens are among the most visible and costly threats to individual and public health. Antibiotics, vaccines, and the molecular revolution in biology have not…
Background A partial differential equation model of population growth and dispersal developed by Lewis and Karieva (1993) predicts that invading populations subject to an…