Past exposure and the dynamics of lymphatic filariasis infection in young children

This study utilizes parallel, longitudinal entomological and parasitological data collected during a 5-year vector control programme in Pondicherry, South India, to quantify Wuchereria bancrofti transmission from the vector to the human population. A simple mathematical model, derived from the standard catalytic model, is used to examine the hypothesis that current infection prevalence in young children is a dynamical function of their cumulative past exposure to infective bites. Maximum likelihood fits of the model to the observed data indicate a constant child infection rate with age, above a threshold representing the pre-patent period, or equivalently, the cumulative biting intensity required to produce patent infections. Extrapolation of the model allows the crude estimation of the equilibrium microfilaria age-prevalence curve due to control. The results suggest that vector control alone may have little impact on the overall age-prevalence of infection even when sustained for long periods. These observations are discussed in terms of the likely impact of density dependent mechanisms, such as acquired immunity, on model predictions.

Re-assessing the global prevalence and distribution of lymphatic filariasis

This paper estimates the global burden of lymphatic filariasis based on a review of the published literature on infection and disease surveys. A method for aggregating and projecting prevalence data from individual studies to national, regional and global levels, which also facilitates the estimation of gender and age-specific burdens, is presented. The method weights in favour of the larger, and hence presumbably more reliable, studies and relies on estimated empirical relationships between gender, age, infection and disease in order to correct studies with incomplete data. The results presented here suggest that although the overall prevalence of filariasis cases is 2.0% globally (approximately totalling 119 million cases), the disease continues to be of considerable local importance, particularly in India and Sub-Saharan Africa. Estimates by age and gender clearly show that, unlike other helminth infections, filariasis is mainly a disease of the adult and older age-classes and appears to be more prevalent in males. This work suggests that the derivation of more accurate estimates of the burden of filariasis will require a better understanding of both the epidemiology and the spatial aspects of infection and disease. It also suggests that filariasis is preventable based on a geographically targeted strategy for control.

Estimation of the fecund life span of Wuchereria bancrofti in an endemic area

A stochastic approach appropriate for general use in endemic communities was applied to estimate the average yearly instantaneous rate of loss of Wuchereria bancrofti microfilaraemia from infected individuals, and gain by uninfected individuals, from longitudinal data. This method was shown to give similar results (i.e., the rate of loss was independent of age, while the rate of gain differed significantly between age classes) to a previously used method based on transmision interruption, provided that the intersurvey interval was > 5 years. The method was used to estimate the fecund life span of W. bancrofti in an endemic area at 5 years. The results suggest that the life span is at the lower end of previous estimates.

Frequency distribution of Wuchereria bancrofti infection in the vector host in relation to human host: evidence for density dependence

This paper uses detailed entomological data from Pondicherry to compare the microfilaria distribution in vector with that of human and also to examine the evidence for the operation of density dependence on parasite transmission. Analysis showed that the distribution in vector is similar to that in human. The expected distribution derived from the fit of a zero-truncated negative binomial to the human data, closely reflected the observed microfilaria distribution in the vector. This implies that a relatively large proportion of observed microfilaria negatives in the vector population may be true zeros, as observed in human, arising from the biting on true negatives (as yet uninfected, with unmated female worms or immune) in humans, rather than attributable to the blood sampling process. Further it was found that both the prevalence of infection and the degree of parasite aggregation in the vector population falls significantly with parasite stage, implying the operation of density dependence, perhaps via parasite-induced vector mortality.

Spatial heterogeneity, nonlinear dynamics and chaos in infectious diseases

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 demographic 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.

Episodic adenolymphangitis and lymphoedema in patients with bancroftian filariasis

In order to explore the relationship between acute and chronic disease, age-specific data on the frequency and duration of episodic adenolymphangitis (ADL) in patients with 3 defined grades of lymphoedema in bancroftian filariasis were examined. The age distribution of grades I and II exhibited a convex age profile, but that of grade III showed a monotonic increase. The mean duration of oedema increased with its grade (grade I, 0.3 years; grade III, 9.9 years). The mean number of ADL episodes in the previous year for all cases was 4.2 and it increased with grade (grade I, 2.4 and grade III, 6.2). The mean duration of each ADL episode for all cases was 4.1 d and it was independent of grade and age. The mean period lost to ADL episodes in the previous year was 17.5 d; it increased from 9.4 d with grade I to 28.5 d with grade III. The results imply that there is a dynamic progression through the grades of lymphoedema and that the frequency of ADL episodes is positively associated with this progression. However, the study design could not separate cause from effect.

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.

Introduction: ecological impact of parasitism on wildlife host populations

The study of parasite population dynamics has been one of the major developments in ecology over the last 15 years (Kennedy, 1975). The seminal articles of Crofton (1971) and Anderson & May (1978, 1979; May & Anderson, 1978, 1979) began this process by illustrating the potential role of parasites in regulating or destabilizing the dynamics of wildlife host populations. Since then, a variety of empirical and theoretical studies (reviewed by Grenfell & Dobson, 1995) have explored the role of parasites in natural populations. In parallel with these population dynamical developments, a growing interest in the evolutionary ecology of parasites has also led to a large literature, examining the evolutionary impact of parasites and the importance of host-parasite coevolution (Hamilton, 1982; May & Anderson, 1990; Lively & Apanius, 1995; Read et al. 1995; Herre, this volume).

Modelling of parasite populations: gastrointestinal nematode models

This paper surveys models of nematode parasites of veterinary importance. A distinction is drawn between generic models which are usually simple formulations applicable to whole classes of parasite and specific models which are often more complex and designed to address questions concerning a particular species. Most of the models considered employ a deterministic framework. Four main groups are considered: generic models of trichostrongylid infection of domestic ruminants, specific models of trichostrongylid infection of domestic ruminants, specific models of experimental laboratory infections of rodents, and a specific model of nematode infections in wildlife.

The association between microfilaraemia and disease in lymphatic filariasis

A standard tenet in the epidemiology of lymphatic filariasis is that patent infection is negatively related to chronic disease. We examine the empirical evidence for this relation by using published data from field studies carried out in a variety of bancroftian filariasis endemic areas. Meta-analysis of the individual study results for each disease category of hydrocele in males only, lymphoedema only, and both conditions combined (total chronic disease) indicate, contrary to expectation, no evidence for a negative association between infection and disease. Indeed, the trend of the empirical evidence is towards the opposite direction, with the majority of studies showing equal propensity of disease in microfilaraemics (mf+ves) and amicrofilaraemics (mf-ves), and more studies indicating a positive rather than a negative relation. There was also a trend for more positive studies for hydrocele compared to lymphoedema. Theoretical analysis suggests that between-study differences in blood sample volumes are unlikely to confound this finding. Analysis of between-study heterogeneity suggests that variations in the local incidence or prevalence of infection rather than unique geographical, including vector, differences might underlie the observed between-study variability in the microfilaraemia-disease association. These results are discussed in terms of dynamic explanations for infection-disease relations in lymphatic filariasis.

Chaos and biological complexity in measles dynamics

Measles epidemiology offers a unique perspective on the construction of models to describe the dynamics of ecological systems. Simple models of measles transmission can generate deterministic chaos by various mechanisms. However, incorporating more biological realism into the model, in the form of age structure and realism in the seasonal forcing function, can suppress complex dynamics. Adding stochastic terms to the models restores complex dynamics, but raises new questions about demographic scale and population structure in these models.

The epidemiology of varicella-zoster virus infections: the influence of varicella on the prevalence of herpes zoster

This paper uses mathematical models and data analysis to examine the epidemiological implications of possible immunologically mediated links between patterns of varicella and herpes-zoster incidence in human communities. A review of previously published reports does not clarify whether or not there is a relationship between the incidence of varicella and the incidence of zoster. However, new analysis of data collected by the Royal College of General Practitioners provides indirect evidence for the hypothesis that a high intensity of varicella transmission suppresses viral reactivation. The significance of this finding for proposed varicella vaccination campaigns is explored by a review of published data on the use of the vaccine. No significant difference is shown to exist between the risk of zoster caused by the vaccine and the wild virus. A mathematical model is then developed to take into consideration the influence of the prevalence of varicella on viral reactivation and the impact of vaccination with attenuated virus, which may be able to recrudesce. Under some conditions, mass application of such vaccines may have the impact of increasing zoster incidence. The results presented here indicate that, before starting any vaccination programme against varicella, its consequences need to be assessed in much more depth.

The epidemiology of varicella-zoster virus infections: a mathematical model

Herpes-zoster is caused by the reactivation of varicella-zoster virus (VZV). In this paper different hypotheses of how this re-emergence of virus comes about are reviewed and discussed. From these hypotheses, and epidemiological data describing the initial transmission of the virus, a mathematical model of primary disease (varicella) and reactivated disease (zoster) in developed countries is derived. The steady-state age distributions of zoster cases predicted by this model are compared with the observed distribution, derived from a review and analysis of published epidemiological data. The model allows differentiation between published hypotheses in which age of host may or may not influence the probability of viral reactivation. The results indicate that the probability of reactivation must increase with age to allow the observed pattern of zoster cases. The basic mathematical model presented provides a conceptual framework, which may be extended to assess possible control programmes.

Infection and disease in lymphatic filariasis: an epidemiological approach

A major question in the study of any parasitic disease is the relationship between infection and clinical disease. The public health importance of lymphatic filariasis has generated a large body of research in this area, both in laboratory studies (Ottesen, 1984,1989; Maizels & Lawrence, 1991) and in the field (Hayashi, 1962; Hairston & Jachowski, 1968; Denham & McGreevy, 1977; Vanamail et al. 1989 b; Bundy, Grenfell & Rajagopalan, 1991; Srividya et al. 1991 b). Despite this, there is still no conclusive explanation for the apparently complex relationship between infection and clinical disease observed in human communities. At least part of the problem may lie in the current impossibility of measuring adult worm burden in vivo (Pichon et al. 1980; Denham & Fletcher, 1987; Das et al. 1990; Grenfell et al. 1990). Although there has recently been significant progress in the development of immuno logical markers for infection status in humans (Ottesen, 1989; Day et al. 1991 a), microfilaraemia is still the most reliable measure of current infection in the field. Studies in endemic areas indicate that, far from there being any simple direct relationship between microfilaraemia and disease status, it is possible to find some individuals with microfilariae in their blood but no disease, and indeed with all other combinations of infection and disease status (Hairston & de-Meillon, 1968; Hairston & Jachowski, 1968; Beaver, 1970; Bryan & Southgate, 1976; Denham & McGreevy, 1977; Pani et al. 1991). Furthermore, the proportions of people in different categories are often observed to vary between endemic areas (Denham & McGreevy, 1977; Day et al. 1991 a).

Overcompensation and population cycles in an ungulate

Although theoretical studies show that overcompensatory density-dependent mechanisms can potentially generate regular or chaotic fluctuations in animal numbers, the majority of realistic single-species models of invertebrate populations are not overcompensatory enough to cause sustained population cycles. The possibility that overcompensation may generate cycles or chaos in vertebrate populations has seldom been considered. Here we show that highly overcompensatng density-dependent mortality can generate recurrent population crashes consistent with those observed in a naturally limited population of Soay sheep. The observed interval of three or more years between crashes points to sharp 'focusing' of mortality over a narrow range of population density.

The population dynamics of nematode infections of ruminants: the effect of seasonality in the free-living stages

A previously published differential equation model for the dynamics of nematode infections of ruminants is modified to allow for time-dependent development and loss rates in the free-living stages. This converts the nonlinear autonomous system to one with periodic coefficients. Fourier transform methods are used to analyse the response of the modified system to these forced oscillations. For biologically reasonable parameter values, the annual pattern of parasitism is determined for the nonautonomous system, and compared with that for the autonomous system with periodic perturbations, and a system incorporating both effects. It is found that, whereas periodic perturbations due to management intervention determine the qualitative annual patterns of larval abundance and host infection, the seasonal dynamics of the larval stages change the magnitude of the adult worm burden.

Frequency distribution of Brugia malayi microfilariae in human populations

This study examines the effects of host age and sex on the frequency distribution of Brugia malayi infections in the human host. Microfilarial (mf) counts for a large data base on the epidemiology of brugian filariasis in Shertallai, Kerala, South India are analysed. Frequency distributions of microfilarial counts partitioned by age are successfully described by zero-truncated negative binomial distributions, fitted by maximum likelihood. This analysis provides estimates of the proportion of mf-positive individuals who are identified as negative due to sampling errors, allowing the construction of corrected mf age-prevalence curves, which indicate that the observed prevalence may under-estimate the true figures by between 18 and 47%. There is no evidence from these results for a decrease in the degree of over-dispersion of parasite frequency distributions with host age, such as might be produced by the acquired immunity to infection. This departure from the pattern in bancroftian filariasis (where there is evidence of such decreases in over-dispersion; Das et al. 1990) is discussed in terms of the long history of filariasis control (and consequently low infection prevalence) in Shertallai.

Immunoepidemiology of lymphatic filariasis: the relationship between infection and disease

Lymphatic filariasis is manifested by a spectrum of symptoms that range from microfilaraemia to gross immunopathology. The geographical variations seen in this disease have been explained by heterogeneity in genetically determined host responses. By modelling the disease through time, Don Bundy, Bryan Grenfell and P.K. Rajagopalan can provide a simple, unified explanation for the observed heterogeneity. Their model shows that there is a sequential progression from infection, microfilaraemia, amicrofilaraemia to obstructive disease in all individuals who experience microfilaraemia. Only the probability of developing microfilaraemia is geographically variable, being dependent on the local incidence of infection.

The dynamics of infection and disease in bancroftian filariasis

This study examines the relationship between the dynamic of Wuchereria bancrofti infection and the development of chronic lymphatic disease. Data sets from Pondicherry, south India, and Calcutta are used to estimate the age-specific proportion of the endemic population which has converted from microfilaria positive to amicrofilaraemia, and is assumed to be at risk of disease. For men, but not women, the age-prevalence profile of the estimated population 'at risk' is shown to correspond closely to the observed age-prevalence of chronic lymphatic disease in the same community. For both sexes, and independent of age, approximately 11% of the population at risk eventually develop lymphoedema. These observations suggest that filariasis endemic populations consist of those individuals who remain amicrofilaraemic and asymptomatic, and those who progress through the sequence: uninfected, microfilaraemic, amicrofilaraemic, to develop irreversible obstructive lymphatic pathology.

Clinical epidemiology of bancroftian filariasis: effect of age and gender

A cross-sectional survey was used to determine the prevalence of disease (n = 6493) and microfilaraemia (n = 24,946) due to Wuchereria bancrofti in Pondicherry, south India. The total disease attributable to filariasis was significantly higher in males (13.67%) than females (2.26%), due to the occurrence of hydrocele in males. While the prevalence of chronic signs was clearly age-dependent in both sexes, that of acute signs was independent of age. Thus the age and gender structure of the survey sample will crucially influence apparent prevalence. Examination of the gender differences in the point prevalence of disease in 12 areas of India showed a significant relationship between occurrence of disease and gender, but this relationship did not significantly differ between northern and southern Indian populations. The study suggested that the failure to appreciate the importance of age and gender in disease prevalence has led to misconception about disease patterns in India.

The population dynamics of nematode infections of ruminants: periodic perturbations as a model for management

We propose and analyse a model for the dynamics of directly transmitted nematode infections of ruminants which allows for the long-term effects of the annual removal of hosts. The model is a simple continuous-time formulation which captures the principal features of parasite transmission and the acquisition of immunity to infection by the host. Analysis of the simplest version of the model, which assumes a constant host population through time, indicates that its equilibrium is locally stable for feasible biological parameters. The regular removal of hosts involved in most management strategies is modelled in terms of periodic perturbations. The analysis indicates that the periodic removal of parasitized hosts corresponds effectively to a reduction in the basic reproductive rate of infection. We also demonstrate that the system exhibits a dramatic peak in parasite numbers during each grazing season at its dynamic equilibrium. This phenomenon (which is characteristically observed in real systems) is discussed in terms of the balance between acquired immunity and periodic perturbations of the parasite population.

Frequency distribution of lymphatic filariasis microfilariae in human populations: population processes and statistical estimation

This paper uses simple mathematical models and statistical estimation techniques to analyse the frequency distribution of microfilariae (mf) in blood samples from human populations which are endemic for lymphatic filariasis. The theoretical analysis examines the relationship between microfilarial burdens and the prevalence of adult (macrofilarial) worms in the human host population. The main finding is that a large proportion of observed mf-negatives may be 'true' zeros, arising from the absence of macrofilarial infections or unmated adult worms, rather than being attributable to the blood sampling process. The corresponding mf distribution should then follow a Poisson mixture, arising from the sampling of mf positives, with an additional proportion of 'true' mf-zeros. This hypothesis is supported by analysis of observed Wuchereria bancrofti mf distributions from Southern India, Japan and Fiji, in which zero-truncated Poisson mixtures fit mf-positive counts more effectively than distributions including the observed zeros. The fits of two Poisson mixtures, the negative binomial and the Sichel distribution, are compared. The Sichel provides a slightly better empirical description of the mf density distribution; reasons for this improvement, and a discussion of the relative merits of the two distributions, are presented. The impact on observed mf distributions of increasing blood sampling volume and extraction efficiency are illustrated via a simple model, and directions for future work are identified.

Frequency distribution of Wuchereria bancrofti microfilariae in human populations and its relationships with age and sex

This paper examines the effects of host age and sex on the frequency distribution of Wuchereria bancrofti infections in the human host. Microfilarial counts from a large data base on the epidemiology of bancroftian filariasis in Pondicherry, South India are analysed. Frequency distributions of microfilarial counts divided by age are successfully described by zero-truncated negative binomial distributions, fitted by maximum likelihood. Parameter estimates from the fits indicate a significant trend of decreasing overdispersion with age in the distributions above age 10; this pattern provides indirect evidence for the operation of density-dependent constraints on microfilarial intensity. The analysis also provides estimates of the proportion of mf-positive individuals who are identified as negative due to sampling errors (around 5% of the total negatives). This allows the construction of corrected mf age-prevalence curves, which indicate that the observed prevalence may underestimate the true figures by between 25% and 100%. The age distribution of mf-negative individuals in the population is discussed in terms of current hypotheses about the interaction between disease and infection.

The relationship between the frequency distribution of Ascaris lumbricoides and the prevalence and intensity of infection in human communities

Observed field data from a range of geographically distinct human communities suggest a consistent non-linear relationship between prevalence and mean intensity of Ascaris lumbricoides infection. Utilizing the negative binomial distribution as a description of observed aggregation, maximum-likelihood analysis reveals that the degree of aggregation is a negative linear function of mean worm burden. The factors responsible for this relationship in human populations require further study but may involve some combination of (i) density-dependent reduction in worm numbers within individuals, (ii) density-dependent parasite-induced host mortality or (iii) self-treatment by heavily infected hosts. Variability in the degree of aggregation appears dependent on the level of infection in a community and independent of geographical differences in the host or parasite populations.