Epidemiology. Foot-and-mouth disease under control in the UK.
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Animals↗
Biomedical subjects
B Grenfell
Publications and source records attributed to B Grenfell.
Stochastic dynamics and a power law for measles variability.
Since the discovery of a power law scaling between the mean and variance of natural populations, this phenomenon has been observed for a variety of species. Here, we show that the same form of power law scaling also occurs in measles case reports in England and Wales. Remarkably this power law holds over four orders of magnitude. We consider how the natural experiment of vaccination affects the slope of the power law. By examining simple generic models, we are able to predict the effects of stochasticity and coupling and we propose a new phenomenon associated with the critical community size.
Demography↗
Inverse density dependence and the Allee effect.
The Allee effect describes a scenario in which populations at low numbers are affected by a positive relationship between population growth rate and density, which increases their likelihood of extinction. The importance of this dynamic process in ecology has been under-appreciated and recent evidence now suggests that it might have an impact on the population dynamics of many plant and animal species. Studies of the causal mechanisms generating Allee effects in small populations could provide a key to understanding their dynamics.
Journal Article↗
Patterns of density dependence in measles dynamics.
An important question in metapopulation dynamics is the influence of external perturbations on the population's long-term dynamic behaviour. In this paper we address the question of how spatiotemporal variations in demographic parameters affect the dynamics of measles populations in England and Wales. Specifically, we use nonparametric statistical methods to analyse how birth rate and population size modulate the negative density dependence between successive epidemics as well as their periodicity. For the observed spatiotemporal data from 60 cities, and for simulated model data, the demographic variables act as bifurcation parameters on the joint density of the trade-off between successive epidemics. For increasing population size, a transition occurs from an irregular unpredictable pattern in small communities towards a regular, predictable endemic pattern in large places. Variations in the birth rate parameter lead to a bifurcation from annual towards biennial cyclicity in both observed data and model data.
Disease Outbreaks↗
Empirical determinants of measles metapopulation dynamics in England and Wales.
A key issue in metapopulation dynamics is the relative impact of internal patch dynamics and coupling between patches. This problem can be addressed by analysing large spatiotemporal data sets, recording the local and global dynamics of metapopulations. In this paper, we analyse the dynamics of measles meta-populations in a large spatiotemporal case notification data set, collected during the pre-vaccination era in England and Wales. Specifically, we use generalized linear statistical models to quantify the relative importance of local influences (birth rate and population size) and regional coupling on local epidemic dynamics. Apart from the proportional effect of local population size on case totals, the models indicate patterns of local and regional dynamic influences which depend on the current state of epidemics. Birth rate and geographic coupling are not associated with the size of major epidemics. By contrast, minor epidemics--and especially the incidence of local extinction of infection--are influenced both by birth rate and geographical coupling. Birth rate at a lag of four years provides the best fit, reflecting the delayed recruitment of susceptibles to school cohorts. A hierarchical index of spatial coupling to large centres provides the best spatial model. The model also indicates that minor epidemics and extinction patterns are more strongly influenced by this regional effect than the local impact of birth rate.
Disease Outbreaks↗
Mathematical and computational challenges in population biology and ecosystems science.
Mathematical and computational approaches provide powerful tools in the study of problems in population biology and ecosystems science. The subject has a rich history intertwined with the development of statistics and dynamical systems theory, but recent analytical advances, coupled with the enhanced potential of high-speed computation, have opened up new vistas and presented new challenges. Key challenges involve ways to deal with the collective dynamics of heterogeneous ensembles of individuals, and to scale from small spatial regions to large ones. The central issues-understanding how detail at one scale makes its signature felt at other scales, and how to relate phenomena across scales-cut across scientific disciplines and go to the heart of algorithmic development of approaches to high-speed computation. Examples are given from ecology, genetics, epidemiology, and immunology.
Acquired Immunodeficiency Syndrome↗
Space, persistence and dynamics of measles epidemics.
This paper explores the relations between persistence and dynamics in measles epidemics. Most current models, including the stochastic seasonally forced and age-structured models examined here, fail to capture simultaneously the observed dynamics and persistence characteristics of epidemics in large urban populations before vaccination. Summary measures of persistence and trienniality allow us to compare epidemics in England, New York and Copenhagen with results of non-spatial and spatial stochastic models. Spatial (metapopulation) structure allow persistence and triennial dynamics to coexist i this class of models. The spatial dynamics of measles, for which detailed spatiotemporal data are available, may serve as a useful test of ideas applicable to other epidemiological and ecological systems with an important spatial component.
Data Interpretation, Statistical↗
Epidemics: models and data.
"The problems of understanding and controlling disease raise a range of challenging mathematical and statistical research topics, from broad theoretical issues to specific practical ones. In particular, recent interest in acquired immune deficiency syndrome has stimulated much progress in diverse areas of epidemic modelling, particularly with regard to the treatment of heterogeneity, both between individuals and in mixing of subgroups of the population. At the same time better data and data analysis techniques have become available, and there have been exciting developments in relevant theory.... This progress in specific areas is now being matched by interdisciplinary cooperation aimed at elucidating relationships between the widely varying types of model that have been found useful, to determine their strengths and limitations in relation to basic aims such as understanding, prediction, and evaluation and implementation of control strategies."
Acquired Immunodeficiency Syndrome↗
Age specific patterns of change in the dynamics of Wuchereria bancrofti infection in Papua New Guinea.
Results of a longitudinal study of the age-specific dynamics of Wuchereria bancrofti infection in a community of East Sepik Province, Papua New Guinea (PNG) are described. Microfilarial (mf) density and serum levels of W. bancrofti phosphorylcholine-containing antigen (PC-Ag) in individuals were used as indirect measures of adult worm burden. These parasitological data were collected from 126 subjects greater than 4 years of age at two time points, 12 months apart, prior to the administration of the antifilarial drug diethylcambamazine (DEC). No significant changes in levels of mf density were observed for the study population between these two time points. However, significant changes in the levels of circulating PC-Ag were noted in subjects less than or equal to 20 years of age, but not in subjects greater than 20 years of age, between these two time points. The apparent shorter half life of circulating PC-Ag compared to that of mf makes antigenemia a more sensitive measure of the dynamics of adult worm populations. These data are discussed in terms of a basic mathematical model describing the dynamics of adult worm populations in relation to their life expectancy and attrition of larvae during establishment. Consideration of these data in the context of this simple immigration/death model suggests that the differences observed in patterns of change in intensity of infection between subjects less than or equal to 20 years old and those greater than 20 years old may be consistent with the acquisition of resistance to superinfection with increasing age.
Adolescent↗
Distinguishing error from chaos in ecological time series.
Over the years, there has been much discussion about the relative importance of environmental and biological factors in regulating natural populations. Often it is thought that environmental factors are associated with stochastic fluctuations in population density, and biological ones with deterministic regulation. We revisit these ideas in the light of recent work on chaos and nonlinear systems. We show that completely deterministic regulatory factors can lead to apparently random fluctuations in population density, and we then develop a new method (that can be applied to limited data sets) to make practical distinctions between apparently noisy dynamics produced by low-dimensional chaos and population variation that in fact derives from random (high-dimensional) noise, such as environmental stochasticity or sampling error. To show its practical use, the method is first applied to models where the dynamics are known. We then apply the method to several sets of real data, including newly analysed data on the incidence of measles in the United Kingdom. Here the additional problems of secular trends and spatial effects are explored. In particular, we find that on a city-by-city scale measles exhibits low-dimensional chaos (as has previously been found for measles in New York City), whereas on a larger, country-wide scale the dynamics appear as a noisy two-year cycle. In addition to shedding light on the basic dynamics of some nonlinear biological systems, this work dramatizes how the scale on which data is collected and analysed can affect the conclusions drawn.
Chickenpox↗