Biomedical subjects

M J Keeling

Publications and source records attributed to M J Keeling.

15 recordsLinked to original sources

PubMed2003

Neighbourhood control policies and the spread of infectious diseases.

We present a model of a control programme for a disease outbreak in a population of livestock holdings. Control is achieved by culling infectious holdings when they are discovered and by the pre-emptive culling of livestock on holdings deemed to be at enhanced risk of infection. Because the pre-emptive control programme cannot directly identify exposed holdings, its implementation will result in the removal of both infected and uninfected holdings. This leads to a fundamental trade-off: increased levels of control produce a greater reduction in transmission by removing more exposed holdings, but increase the number of uninfected holdings culled. We derive an expression for the total number of holdings culled during the course of an outbreak and demonstrate that there is an optimal control policy, which minimizes this loss. Using a metapopulation model to incorporate local clustering of infection, we examine a neighbourhood control programme in a locally spreading outbreak. We find that there is an optimal level of control, which increases with increasing basic reproduction ratio, R(0); moreover, implementation of control may be optimal even when R(0) < 1. The total loss to the population is relatively insensitive to the level of control as it increases beyond the optimal level, suggesting that over-control is a safer policy than under-control.

Animals↗

PubMed2003

The invasion and coexistence of competing Wolbachia strains.

Cytoplasmic incompatibility between arthropods infected with different strains of Wolbachia has been proposed as an important mechanism for speciation. However, a basic requirement for this mechanism is the coexistence of different strains in neighbouring populations. Here we test whether this required coexistence is possible in a spatial context. Continuous-time models for the behaviour of one and two strains of Wolbachia within a single well-mixed population demonstrate the Allee effect and founder control, such that one strain is always driven extinct. In contrast, discretised spatial models show patchy persistence of the two strains although coexistence within the same habitat is rare. A simplified model of such founder control suggests that it is fragmentation of (or barriers within) the habitat rather than space itself that leads to persistence.

Models, Biological↗

PubMed2002

Modelling vaccination strategies against foot-and-mouth disease.

Vaccination has proved a powerful defence against a range of infectious diseases of humans and animals. However, its potential to control major epidemics of foot-and-mouth disease (FMD) in livestock is contentious. Using an individual farm-based model, we consider either national prophylactic vaccination campaigns in advance of an outbreak, or combinations of reactive vaccination and culling strategies during an epidemic. Consistent with standard epidemiological theory, mass prophylactic vaccination could reduce greatly the potential for a major epidemic, while the targeting of high-risk farms increases efficiency. Given sufficient resources and preparation, a combination of reactive vaccination and culling might control ongoing epidemics. We also explore a reactive strategy, 'predictive' vaccination, which targets key spatial transmission loci and can reduce markedly the long tail that characterizes many FMD epidemics. These analyses have broader implications for the control of human and livestock infectious diseases in heterogeneous spatial landscapes.

Animals↗

PubMed2001

Dynamics of the 2001 UK foot and mouth epidemic: stochastic dispersal in a heterogeneous landscape.

Foot-and-mouth is one of the world's most economically important livestock diseases. We developed an individual farm-based stochastic model of the current UK epidemic. The fine grain of the epidemiological data reveals the infection dynamics at an unusually high spatiotemporal resolution. We show that the spatial distribution, size, and species composition of farms all influence the observed pattern and regional variability of outbreaks. The other key dynamical component is long-tailed stochastic dispersal of infection, combining frequent local movements with occasional long jumps. We assess the history and possible duration of the epidemic, the performance of control strategies, and general implications for disease dynamics in space and time.

Animal Husbandry↗

PubMed2000

Reinterpreting space, time lags, and functional responses in ecological models.

Natural enemy-victim interactions are of major applied importance and of fundamental interest to ecologists. A key question is what stabilizes these interactions, allowing the long-term coexistence of the two species. Three main theoretical explanations have been proposed: behavioral responses, time-dependent factors such as delayed density dependence, and spatial heterogeneity. Here, using the powerful moment-closure technique, we show a fundamental equivalence between these three elements. Limited movement by organisms is a ubiquitous feature of ecological systems, allowing spatial structure to develop; we show that the effects of this can be naturally described in terms of time lags or within-generation functional responses.

Animals↗

PubMed2000

Bubonic plague: a metapopulation model of a zoonosis.

Bubonic plague (Yersinia pestis) is generally thought of as a historical disease; however, it is still responsible for around 1000-3000 deaths each year worldwide. This paper expands the analysis of a model for bubonic plague that encompasses the disease dynamics in rat, flea and human populations. Some key variables of the deterministic model, including the force of infection to humans, are shown to be robust to changes in the basic parameters, although variation in the flea searching efficiency, and the movement rates of rats and fleas will be considered throughout the paper. The stochastic behaviour of the corresponding metapopulation model is discussed, with attention focused on the dynamics of rats and the force of infection at the local spatial scale. Short-lived local epidemics in rats govern the invasion of the disease and produce an irregular pattern of human cases similar to those observed. However, the endemic behaviour in a few rat subpopulations allows the disease to persist for many years. This spatial stochastic model is also used to identify the criteria for the spread to human populations in terms of the rat density. Finally, the full stochastic model is reduced to the form of a probabilistic cellular automaton, which allows the analysis of a large number of replicated epidemics in large populations. This simplified model enables us to analyse the spatial properties of rat epidemics and the effects of movement rates, and also to test whether the emergent metapopulation behaviour is a property of the local dynamics rather than the precise details of the model.

Animals↗

PubMed2000

Metapopulation dynamics of bubonic plague.

Bubonic plague is widely regarded as a disease of mainly historical importance; however, with increasing reports of incidence and the discovery of antibiotic-resistant strains of the plague bacterium Yersinia pestis, it is re-emerging as a significant health concerns. Here we bypass the conventional human-disease models, and propose that bubonic plague is driven by the dynamics of the disease in the rat population. Using a stochastic, spatial metapopulation model, we show that bubonic plague can persist in relatively small rodent populations from which occasional human epidemics arise, without the need for external imports. This explains why historically the plague persisted despite long disease-free periods, and how the disease re-occurred in cities with tight quarantine control. In a contemporary setting, we show that human vaccination cannot eradicate the plague, and that culling of rats may prevent or exacerbate human epidemics, depending on the timing of the cull. The existence of plague reservoirs in wild rodent populations has important public-health implications for the transmission to urban rats and the subsequent risk of human outbreaks.

Animals↗

PubMed2000

Multiplicative moments and measures of persistence in ecology.

Ecologists and epidemiologists have begun focusing on demographic stochasticity and spatial heterogeneity as important biological factors. With high-powered computers simulation of such systems is a common modelling technique; however we lack a detailed understanding of the processes involved. Moment closure approximations provide a simple method which can be used to capture the main features of a wide variety of stochastic models and to gain a more intuitive understanding. In this paper we give an alternative variation based on multiplicative moments which is equivalent to taking a novel third-order cumulant approximation. The differential equations for these multiplicative moments are far more robust than their additive counterparts. We use this technique to consider the behaviour and persistence of finite metapopulations for two common ecological systems.

Animals↗

PubMed2000

Individual-based perspectives on R(0).

Without doubt the basic reproductive ratio, R(0), is the most widely used quantity in epidemic theory. Standard compartmental models show how R(0)is related to the average age of infection, vaccination thresholds for eradication and equilibrium solutions. However, many of the basic formulae for R(0)break down when we consider transmission of infection to be a stochastic process involving discrete individuals. This paper clarifies why and when these differences arise and predicts when individual-based considerations are likely to be important in modelling infection dynamics.

Disease Outbreaks↗

PubMed2000

Simple stochastic models and their power-law type behaviour.

A power-law relationship between the mean and variance of ecological time series has been shown to hold for a vast number of species. Here we examine the behaviour of single-species stochastic models and concentrate in particular on the mean-variance relationship as the carrying capacity becomes large. Single-species stochastic models can be written as Markov chains, and the long-term distribution of population sizes and hence power-law scaling can be found analytically. The various power-law scalings that arise have very different biological implications for the effects of stochasticity and the departure from the deterministic paradigm. Finally we extend our analysis to consider the complicating factors of spatial heterogeneity, nontrivial deterministic dynamics, and multispecies models.

Bias↗

PubMed1999

The effects of local spatial structure on epidemiological invasions.

Predicting the likely success of invasions is vitally important in ecology and especially epidemiology. Whether an organism can successfully invade and persist in the short-term is highly dependent on the spatial correlations that develop in the early stages of invasion. By modelling the correlations between individuals, we are able to understand the role of spatial heterogeneity in invasion dynamics without the need for large-scale computer simulations. Here, a natural methodology is developed for modelling the behaviour of individuals in a fixed network. This formulation is applied to the spread of a disease through a structured network to determine invasion thresholds and some statistical properties of a single epidemic.

Communicable Disease Control↗

PubMed1998

Effect of variability in infection period on the persistence and spatial spread of infectious diseases.

The effects of the mean infection (incubation plus infectious) period on the dynamics of infectious diseases are well understood. We examine the dynamics and persistence of epidemics when the distribution of the infection period also is modelled, using the well-documented childhood disease measles as a test case. We pay particular attention to the differences between exponentially distributed and constant periods. The use of constant periods increases the persistence of epidemics by reducing the individual stochasticity. The infection period distribution is also shown to have a significant effect on the spatial spread of disease.

Child↗

PubMed1997

Correlation models for childhood epidemics.

One of the simplest set of equations for the description of epidemics (the SEIR equations) has been much studied, and produces reasonable approximations to the dynamics of communicable disease. However, it has long been recognized that spatial and social structure are important if we are to understand the long-term persistence and detailed behaviour of disease. We will introduce three pair models which attempt to capture the underlying heterogeneous structure by studying the connections and correlations between individuals. Although modelling the correlations necessarily leads to more complex equations, this pair formulation naturally incorporates the local dynamical behaviour generating more realistic persistence. In common with other studies on childhood diseases we will focus our attention on measles, for which the case returns are particularly well documented and long running.

Age Distribution↗

PubMed1997

Disease extinction and community size: modeling the persistence of measles.

A basic issue in ecology is the relation between extinction and population size. One of the clearest manifestations of a population threshold for extinction is the critical community size below which infections like measles do not persist. The current generation of stochastic models overestimates the observed critical community size for measles, generating much less persistence of infection than is observed. The inclusion of a more biologically realistic model for the duration of infection produced a much closer fit to the actual critical community size and explains previously undescribed high-frequency oscillations in measles incidence.

Adolescent↗

PubMed1997

Modelling the persistence of measles.

For vaccination programs to be effective, it is important to understand and predict the persistence of the disease. By considering the process at different scales (from the individual to the population level), several models allow the persistence of diseases, such as measles, to be captured.

Genetic Heterogeneity↗