R. M. Anderson

Processes influencing the distribution of parasite numbers within host populations with special emphasis on parasite-induced host mortalities.

The paper examines the factors which generate various patterns of dispersion in the distribution of parasites within their host populations. Particular emphasis is placed on the role played by chance elements in the growth and decay of parasite populations and on the influence of different types of demographic processes. It is argued that observed distributions are dynamic, rather than static, entities generated by opposing forces, some acting to create over-dispersion and others acting to generate under-dispersion. Monte Carlo simulation experiments, based on probability models of the growth and decay of host and parasite populations, are used to study the dynamics of parasite dispersion. Attention is specifically focused on the role played by parasite-induced host mortality. It is shown that, for certain types of host-parasite associations, convex curves of mean parasite abundance in relation to age (age-intensity curves), concomitant with a decline in the degree of dispersion in the older age, classes of hosts, may be evidence of the induction in host mortality by parasite infection. Empirical evidence is examined in light of this prediction. In general, however, simulation studies highlight the technical difficulties inherent in establishing clear evidence of parasite-induced host mortality from ecological studies of hosts and parasites in their natural habitats.

Immunisation and herd immunity

This paper sketches how mathematical models that are soundly based on epidemiological data can help us understand the effects upon population-level or «heard» immunity of specific immunisation policies. Some of the questions that can be illuminated within such an analytic framework are: What proportion of the population should be immunised to achieve eradication (locally or globally)? How is this affected by birth rates and other demographic factors? What is the best age to immunise? How does mass immunisation affect the age distribution of susceptible individuals, particularly in those age-classes most at risk from serious diseases? How significant are genetic, social, or spatial heterogeneities in susceptibility or exposure to infection? And how does this affect herd immunity?

Parasite—host coevolution

In this paper we wish to develop three themes, each having to do with evolutionary aspects of associations between hosts and parasites (with parasite defined broadly, to include viruses, bacteria and protozoans, along with the more conventionally defined helminth and arthropod parasites). The three themes are: the evolution of virulence; the population dynamics and population genetics of host–parasite associations; and invasions by, or ‘emergence’ of, new parasites.

The population dynamics of Gyrodactylus bullatarudis (Monogenea) within laboratory populations of the fish host Poecilia reticulata

Experiments were undertaken to investigate the factors which influence the transmission dynamics of Gyrodactylus bullatarudis within populations of laboratory guppies. The parasites possess a number of biological attributes which are almost unique amongst helminth parasites of vertebrates. These include the ability to reproduce viviparously and directly on the surface of the host, the ability to survive death of the host (for a short period of time) and the ability to transfer between hosts (despite the absence of a specialized transmission stage in the parasites life-cycle). Long-term laboratory experiments demonstrated the inability of the parasite to persist within populations of the host in the absence of the continual introduction of naive susceptible fish. With regular addition of susceptible fish, the parasite population exhibited recurrent epidemic behaviour. The magnitudes of the epidemics and the time interval between them, were dependent on the rate at which fish were added to the populations. The parasite was over-dispersed in its distribution within the experimental fish populations and was a significant cause of host mortality (in a manner related to parasite burden). The experimental results suggest that acquired resistance to infection is an important factor determining epidemic behaviour.

Prevalence of schistosome infections within molluscan populations: observed patterns and theoretical predictions.

The paper draws together a large and scattered body of empirical evidence concerning the prevalence of snail infection with schistosome parasites in field situations, the duration of the latent period of infection in snails (and its dependence on temperature), and the mortality rates of infected and uninfected snails in field and laboratory conditions. A review and synthesis of quantitative data on the population biology of schistosome infections within the molluscan host is attempted and observed patterns of infection are compared with predictions of a schistosomiasis model developed by May (1977) which incorporates differential snail mortality (between infected and uninfected snails) and latent periods of infection. It is suggested that the low levels of prevalence within snail populations in endemic areas of schistosomiasis are closely associated with high rates of infected snail mortality and the duration of the latent period of infection within the mollusc. In certain instances, the expected life-span of an infected snail may be less than the duration of the latent period of infection. Such patterns generate very low levels of parasite prevalence. A new age prevalence model for schistosome infections within snail populations is developed and its predictions compared with observed patterns. The implications of this study of observed and predicted patterns of snail infection within molluscan populations are discussed in relation to the overall transmission dynamics of schistosomiasis.

Non-linear phenomena in host—parasite interactions

The paper examines non-linear dynamical phenomena in host-parasite interactions by reference to a series of different problems ranging from the impact on transmission of control measures based on vaccination and chemotherapy, to the effects of immunological responses targeted at different stages in a parasites life-cycle. Throughout, simple mathematical models are employed to aid in interpretation. Analyses reveal that the influence of a defined control measure on the prevalence or intensity of infection, whether vaccination or drug treatment, is non-linearly related to the magnitude of control effort (as defined by the proportion of individuals vaccinated or treated with a drug). Consideration of the relative merits of gametocyte and sporozoite vaccines against malarial parasites suggests that very high leves of cohort immunization will be required to block transmission in endemic areas, with the former type of vaccine being more effective in reducing transmission for a defined level of coverage and the latter being better with respect to a reduction in morbidity. The inclusion of genetic elements in analyses of the transmission of helminth parasites reveals complex non-linear patterns of change in the abundance of different parasite genotypes under selection pressures imposed by either the host immunological defences or the application of chemotherapeutic agents. When resistance genes are present in parasite populations, the degree to which abundance can be suppressed by chemotherapy depends critically on the frequency and intensity of application, with intermediate values of the former being optimal. A more detailed consideration of the impact of immunological defences on parasite population growth within an individual host, by reference to the erythrocytic cycle of malaria, suggests that the effectiveness of a given immunological response is inversely related to the life-expectancy of the target stage in the parasites developmental cycle.

Estimating the human health risk from possible BSE infection of the British sheep flock

Following the controversial failure of a recent study and the small numbers of animals yet screened for infection, it remains uncertain whether bovine spongiform encephalopathy (BSE) was transmitted to sheep in the past via feed supplements and whether it is still present. Well grounded mathematical and statistical models are therefore essential to integrate the limited and disparate data, to explore uncertainty, and to define data-collection priorities. We analysed the implications of different scenarios of BSE spread in sheep for relative human exposure levels and variant Creutzfeldt–Jakob disease (vCJD) incidence. Here we show that, if BSE entered the sheep population and a degree of transmission occurred, then ongoing public health risks from ovine BSE are likely to be greater than those from cattle, but that any such risk could be reduced by up to 90% through additional restrictions on sheep products entering the food supply. Extending the analysis to consider absolute risk, we estimate the 95% confidence interval for future vCJD mortality to be 50 to 50,000 human deaths considering exposure to bovine BSE alone, with the upper bound increasing to 150,000 once we include exposure from the worst-case ovine BSE scenario examined.

The dynamics of infection of Tribolium confusum by Hymenolepis diminuta: the influence of infective-stage density and spatial distribution.

The mean parasite burden of a population of Tribolium confusum is shown to rise to a plateau as the exposure density of infective eggs of Hymenolepis diminuta increases. The level of this plateau is shown to be dependent on the nutritional status of the host population, being depressed from approximately 18 cysticeroids/beetle in hosts which have been starved prior to experimentation, to approximately 2 cysticercoids/beetle in satiated hosts. A simple model is used to describe the shape of this infection functional response in terms of the predator-prey interaction between hosts (T. confusum) and parasite infective stages (H. diminuta eggs). The distribution of successful infections/host is shown to be over-dispersed, even when hosts are exposed to infective stages arranged in a uniform spatial pattern. The over-dispersion of parasite numbers/host is shown to become more severe as the spatial pattern of infective stages changes from under-dispersed, through random, to over-dispersed. Experimental results are discussed in relation to the dynamics of parasite-host interactions, in which infection takes place by host ingestion of a free-living infective stage.

Transmission of Schistosoma mansoni from man to snail: experimental studies of miracidial survival and infectivity in relation to larval age, water temperature, host size and host age

We report the results of experimental work on (a) the influence of temperature on the age-dependent survival and infectivity of the miracidia of Schistosoma mansoni and (b) the relationship between snail age, snail size and susceptibility to infection. The death rate of miracidia declined exponentially with age where life-expectancy was maximal (approximately 16 h) at 15 degrees C. Infectivity also declined rapidly with larval age but, in contrast to larval survival, the rate of infection was at a maximum at 25 degrees C. Snail susceptibility was shown to be more closely correlated with host size rather than host age. Susceptibility declined exponentially with increased host size. Size-dependent susceptibility was shown to generate concave age-prevalence curves for infection within snail populations, where the maximum prevalence is generated in snails of intermediary age. Simple mathematical models are developed to aid estimation of larval survival and infection rates and experimental results are discussed in relation to the overall transmission success of the parasite from man to snail.

Theoretical basis for the use of pathogens as biological control agents of pest species

The population dynamics of insect–pathogen interactions are examined with the aid of simple mathematical models. Three concepts of central importance to the interpretation of population behaviour are discussed, namely the ability of the pathogen to persist within its host population, the ability to regulate and depress host population abundance, and the ability to induce non-seasonal cyclic changes in host density. The selection of pathogen species or strains to depress pest population growth is discussed and the optimal characteristics are shown to be intermediate pathogencity combined with an ability to reduce infected host reproduction, high transmission efficiency, including elements of vertical as well as horizontal transmission stages. When the pathogen plays a significant role in the regulation of host population growth, it is argued that many insect–pathogen interactions will exhibit non-seasonal oscilations in host and pathogen abundance. Mathematical models are used to explore the patterns of population behaviour that result from the continual introduction of a pathogen into a target pest population. It is shown that there exists a critical introdution rate, above which the eradication of the pest is theoretically possible. Significant reductions in pest population abundance will not occur until the introduction rate approaches this critical value, whereupon the oscillatory behaviour of the interaction between host and pathogen population will be suppressed. A general dicussion is given of the problems arising from the combined use of chemical agents and pathogens for the control of pest species, and the evolutionary pressures acting on host and pathogen populations.