Spatial parasite transmission, drug resistance, and the spread of rare genes.

The transmission of many parasitic worms involves aggregated movement between hosts of "packets" of infectious larvae. We use a generic metapopulation model to show that this aggregation naturally promotes the preferential spread of rare recessive genes, compared with the expectations of traditional nonspatial models. A more biologically realistic model also demonstrates that this effect could explain the rapid observed spread of recessive or weakly dominant drug-resistant genotypes in nematode parasites of sheep. This promotion of a recessive trait arises from a novel mechanism of inbreeding arising from the metapopulation dynamics of transmission.

Floods: some probabilistic and statistical approaches.

Some of the many statistical aspects of floods are discussed and some new results are given on a number of features. The probability theory of extreme values is briefly reviewed and its potential for applications outlined. The peaks-over-threshold method of estimation is compared with the direct use of annual maxima and some theoretical comparisons of efficiency are given. The effect of trend on the distribution of maxima is analysed in terms of a simple theoretical model distinguishing the effects of trend in mean level and of trend in dispersion. An empirical Bayes method for pooling information from a number of sources is described and illustrated, and related to the procedures recommended in the Flood estimation handbook. In the final section, a range of further issues is outlined.

Drug-resistant parasites and aggregated infection--early-season dynamics.

We investigate the effect of spatial aggregation in the infection dynamics of nematode parasites in ruminants. We show that a high degree of spatial aggregation is likely to lead to a dramatically enhanced rate of invasion by drug-resistant strains.

Disease surveillance and data collection issues in epidemic modelling.

This paper is founded on a tutorial session given to the School on Modern Statistical Methods in Medical Research which was held at the International Centre for Theoretical Physics, Trieste in September 1999. We review the aims, scope and purposes of infectious disease surveillance including determining transmission information to underpin model structure and parameterization in epidemic modelling. The practical problems inherent in collecting surveillance data are illustrated by a study of HIV/AIDS in Cambodia. We also review the basic elements of mathematical models developed to represent the transmission dynamics of infectious diseases, and discuss reasons for the gap between mathematical epidemic models and available data.

Stochastic simulation and the detection of immunity to schistosome infections.

In this paper we address the question of detecting immunity to helminth infections from patterns of infection in endemic communities. We use stochastic simulations to investigate whether it would be possible to detect patterns predicted by theoretical models, using typical field data. Thus, our technique is to simulate a theoretical model, to generate the data that would be obtained in field surveys and then to analyse these data using methods usually employed for field data. The general behaviour of the model, and in particular the levels of variability of egg counts predicted, show that the model is capturing most of the variability present in field data. However, analysis of the data in detail suggests that detection of immunity patterns in real data may be very difficult even if the underlying patterns are present. Analysis of a real data set does show patterns consistent with acquired immunity and the implications of this are discussed.

A stochastic model of schistosomiasis immuno-epidemiology.

Schistosomiasis is a helminth (worm) infection with approximately 200 million people infected worldwide. There is still controversy on whether differing worm burdens between individuals is a result of differing contact rates or of acquired immunity. In this paper, we present a stochastic modelling framework to address these issues. By using appropriate approximations for the higher moments of the joint distributions, differential equations for the means, variances and co-variances of infection and immunity can be obtained. Numerical solutions of these equations to obtain age profiles of the above properties were compared with Monte Carlo simulations of the stochastic process. Simulations showed that the results depended on whether between host heterogeneity was generated by differing contact rates or differing immune responses. Heterogeneity in contact rates produced a highly aggregated distribution of parasites with a large variance/mean ratio. Heterogeneity in the immune response had very little effect on the overall dynamics. This agrees with the predominant field evidence which would suggest that infection is mainly determined by ecology with a smaller contribution of immunity.

Modelling variability in lymphatic filariasis: macrofilarial dynamics in the Brugia pahangi--cat model.

A striking feature of lymphatic filariasis is the considerable heterogeneity in infection burden observed between hosts, which greatly complicates the analysis of the population dynamics of the disease. Here, we describe the first application of the moment closure equation approach to model the sources and the impact of this heterogeneity for macrofilarial population dynamics. The analysis is based on the closest laboratory equivalent of the life cycle and immunology of infection in humans--cats chronically infected with the filarial nematode Brugia pahangi. Two sets of long-term experiments are analysed: hosts given either single primary infections or given repeat infections. We begin by quantifying changes in the mean and aggregation of adult parasites (inversely measured by the negative binomial parameter, kappa in cohorts of hosts using generalized linear models. We then apply simple stochastic models to interpret observed patterns. The models and empirical data indicate that parasite aggregation tracks the decline in the mean burden with host age in primary infections. Conversely, in repeat infections, aggregation increases as the worm burden declines with experience of infection. The results show that the primary infection variability is consistent with heterogeneities in parasite survival between hosts. By contrast, the models indicate that the reduction in parasite variability with time in repeat infections is most likely due to the 'filtering' effect of a strong, acquired immune response, which gradually acts to remove the initial variability generated by heterogeneities in larval mortality. We discuss this result in terms of the homogenizing effect of host immunity-driven density-dependence on macrofilarial burden in older hosts.

Modelling patterns of parasite aggregation in natural populations: trichostrongylid nematode-ruminant interactions as a case study.

The characteristically aggregated frequency distribution of macroparasites in their hosts is a key feature of host-parasite population biology. We begin with a brief review of the theoretical literature concerning parasite aggregation. Though this work has illustrated much about both the sources and impact of parasite aggregation, there is still no definite analysis of both these aspects. We then go on to illustrate the use of one approach to this problem--the construction of Moment Closure Equations (MCEs), which can be used to represent both the mean and second moments (variances and covariances) of the distribution of different parasite stages and phenomenological measures of host immunity. We apply these models to one of the best documented interactions involving free-living animal hosts--the interaction between trichostrongylid nematodes and ruminants. The analysis compares patterns of variability in experimental infections of Teladorsagia circumcincta in sheep with the equivalent wildlife situation--the epidemiology of T. circumcincta in a feral population of Soay sheep on St Kilda, Outer Hebrides. We focus on the relationship between mean parasite load and aggregation (inversely measured by the negative binomial parameter, k) for cohorts of hosts. The analysis and empirical data indicate that k tracks the increase and subsequent decline in the mean burden with host age. We discuss this result in terms of the degree of heterogeneity in the impact of host immunity or parasite-induced mortality required to shorten the tail of the parasite distribution (and therefore increase k) in older animals. The model is also used to analyse the relationship between estimated worm and egg counts (since only the latter are often available for wildlife hosts). Finally, we use these results to review directions for future work on the nature and impact of parasite aggregation.