Introduction

Hydatid disease is caused by accidental infection with the intermediate stages of tapeworms of Echinococcus species, principally Echinococcus granulosus and E.multilocularis. The adult worm parasitises the small intestine of carnivores, usually Canidae, and sheds proglottids containing eggs which pass with the host's faeces. If the eggs are then ingested by a herbivore they develop into a larval stage (cyst) within the liver or other viscera. The cycle is completed when the carnivore consumes the herbivore, ingesting a mature cyst. Echinococcus granulosus originated in a wolf-deer life-cycle, and has evolved in dogs and sheep and other domesticated and wild animals. The definitive hosts of E.multilocularis are foxes, and the intermediate hosts small rodents such as voles and lemmings. Echinococcus granulosus is ubiquitous but E.multilocularis is confined to the Northern Hemisphere. Cystic hydatid disease in man is caused by the larval form of E.granulosus. Surgery provides a cure in 50–90% of cases, but recurrence is common. Alveolar hydatid disease caused by E.multilocularis results in metastases throughout the soft organs. Until recently it was invariably fatal, but chemotherapy may retard the proliferation of cysts. For further information on the epidemiology of echinococcosis and hydatid disease see Roberts and Gemmell (1994). This paper presents two examples where models of the dynamics of Echinococcus species have been used to investigate control policies.

Echinococcus granulosusin farmed animals in New Zealand.

The first case of cystic hydatid disease in New Zealand was recorded in 1862. The annual number of cases peaked at 7.2 per 100,000 in 1946, and then declined to 0.37 per 100,000 in 1987, largely due to the control programme that was initiated in 1959. From that time all dogs were subjected to regular chemotherapy to remove tapeworms.

Introduction

In this chapter we review some of the basic theory of deterministic modelling of microparasitic diseases of wild animal populations. As discussed by Dobson and Grenfell in the Introduction to this volume, the special feature of wildlife diseases is that host population size is a dynamic variable. This requires significant modifications to classical epidemic theory based on constant host populations. Particularly since the seminal work of Anderson and May (1979), there has been a large body of research in this area (reviewed by Barlow, Begon and Bowers, Briggs et al. (this volume)). Here we review some basic issues in the modelling of microparasitic infections in naturallyfluctuating animal populations. The paper is not intended as an in depth study of microparasite models, but should be seen more as a summer exhibition at a museum with little bits of everything, as a guide to the art of elementary modelling and the less accessible more mathematical literature where the exhibits are usually stored.

There are many purposes for using mathematical models in epidemiology (see Anderson and May (1991), Hethcote and Van Ark (1992) for an extensive list). Among the main ‘justifications’ are, firstly, the fact that models provide insight into the relative importance of factors that influence spread, and improve our understanding of the relationship between mechanisms that operate on the level of the individual and the phenomena that result on the population-level (after Diekmann 1991). Secondly, the formulation of mathematical models requires precision about the underlying hypothesis and could make one aware of working hypotheses that might otherwise go unnoticed and which, once discovered, might deserve scrutiny.

Introduction

Quantitative approaches to parasite population biology can be broadly classified into two research areas. The first body of work is essentially epidemiological, concentrating mainly on infections of humans (Anderson and May 1991) and managed farm animals. A major focus here is the role of host immunity in determining patterns of infection, particularly in the case of long-lived helminth parasites (Quinnell and Keymer 1990). This area has recently received considerable theoretical attention, particularly in the derivation of immuno-epidemiological models, which seek to account for parasite age-intensity profiles in terms of simple phenomenological models for immunity (Anderson and May 1985a, Grenfell and Michael 1992, Woolhouse 1992).

The second area (and the subject of this volume) is essentially an ecological examination of the interaction of parasites with their (naturally-fluctuating) host populations (Anderson and May 1978, May and Anderson 1978). Unlike many human infections, where host dynamics can often be neglected, the focus here is on the dynamics of the host-parasite interaction (Roberts et al. this volume) and, increasingly, with questions of coevolution (Lively and Apanius, this volume). In terms of host-macroparasite population dynamics, a crucial issue is the balance between parasite induced host mortality and reproductive limitations due to parasitism (which tend respectively to stabilize and destabilize host dynamics (Anderson and May 1978, May and Anderson 1978). The statistical distribution of parasites among hosts has a major impact on both the above areas.

Introduction

The nature of macroparasitic infections

Parasites harm their hosts (Figure 1). That is one of the reasons we are interested in them. The notion that parasitism had some adverse effect on the mortality or fecundity of the host was an explicit part of Anderson and May's definition of the relationship (Anderson and May 1978), but is often attacked on the grounds that many host-parasite relationships seem to result in no discernable harm to the host. It is not difficult to find instances in the literature (usually case studies) in which individual animals or sometimes whole populations are found to have died as a result of infection with one or more species of parasite. Examples include dolphins and killer whales that have become stranded because nematode or trematode infections of the eustachian tube or cochlea have interfered with echolocation (Dailey and Ridgeway 1976, Stroud and Roffe 1979, Morimitsu et al. 1987); anaemia and pneumonia caused by excessively large nematode burdens resulting in the death of an opossum (Nettles, Prestwood and Davidson 1975); a similarly overwhelming trematode infection causing the death of a cougar (Kistner et al. 1979); and nematode infections as the cause of substantial mortality in populations of egrets and white tailed deer (Wiese et al. 1977, Davidson et al. 1980). Such instances are often dismissed as involving unusually high levels of parasitism or abnormal or aberrant hosts and are contrasted with those studies which report no discernable consequences of parasitism.