This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Add to Saved Citations Download to citation manager Request Permissions Request Reprints Add to My Marked Citations Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Grenfell, B. Articles by Bolker, B. Search for Related Content PubMed PubMed Citation Articles by Grenfell, B. Articles by Bolker, B. Pubmed/NCBI databases Medline Plus Health Information Infectious Diseases Social Bookmarking                         What's this?

Spatial heterogeneity, nonlinear dynamics and chaos in infectious diseases

Zoology Department, Cambridge University

A. Kleczkowski

Department of Plant Sciences, Cambridge University, Cambridge, UK

CA Gilligan

Department of Plant Sciences, Cambridge University, Cambridge, UK

BM Bolker

Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey, USA

There is currently considerable interest in the role of nonlinear phenomena in the population dynamics of infectious diseases. Childhood diseases such as measles are particularly well documented dynamically, and have recently been the subject of analyses (of both models and notification data) to establish whether the pattern of epidemics is chaotic. Though the spatial dynamics of measles have also been extensively studied, spatial and nonlinear dynamics have only recently been brought together. The present review concentrates mainly on describing this synthesis. We begin with a general review of the nonlinear dynamics of measles models, in a spatially homogeneous environment. Simple compartmental models (specifically the SEIR model) can behave chaotically, under the influence of strong seasonal 'forcing' of infection rate associated with patterns of schooling. However, adding observed heterogeneities such as age structure can simplify the deterministic dynamics back to limit cycles. By contrast all current strongly seasonally forced stochastic models show large amplitude irregular fluctuations, with many more 'fadeouts' of infection that is observed in real communities of similar size. This indicates that (social and/ or geographical) spatial heterogeneity is needed in the models. We review the exploration of this problem with nonlinear spatiotemporal models. The few studies to date indicate that spatial heterogeneity can help to increase the realism of models. However, a review of nonlinear analyses of spatially subdivided measles data show that more refinements of the models (particularly in representing the impact of human demo graphic changes on infection dynamics) are required. We conclude with a discussion of the implication of these results for the dynamics of infectious diseases in general and, in particular, the possibilities of cross fertilization between human disease epidemiology and the study of plant and animal diseases.

Statistical Methods in Medical Research, Vol. 4, No. 2, 160-183 (1995)
DOI: 10.1177/096228029500400205


CiteULike    Complore    Connotea    Del.icio.us    Digg    Reddit    Technorati    Twitter    What's this?

This article has been cited by other articles:

				A. J.K Conlan and B. T Grenfell Seasonality and the persistence and invasion of measles Proc R Soc B, May 7, 2007; 274(1614): 1133 - 1141. [Abstract] [Full Text] [PDF]