The role of mathematical models in helminth population biology

This brief review aims to illustrate how theory can aid in our understanding of the factors that determine the regulation and stability of parasite abundance, and influence the impact of control measures. The current generation of models are obviously crude, and ignore much biological detail, but they are often able to capture qualitative trends observed in real communities. As such, their analysis and investigation can provide important conceptional insights or, in some circumstances, they can be of value in a predictive role (e.g. the impact of chemotherapy in human communities).This field of research, however, is still in its infancy and much remains to be done to improve biological realism in model formulation and to extent the methods of analysis and interpretation. In the latter context, for example, the current analytical methods for the study of the dynamical properties of non-linear systems of differential and partial differential equations are inadequate for many areas of biological application. Future advances in applied mathematics will, therefore, be of great importance. As far as biological realism is concerned, three areas require urgent attention. The first concerns the treatment of heterogeneity in worm loads within host communities. The generative factors of parasite aggregation are many and varied and little is understood at present of how these processes influence a parasite's population response to perturbation induced, for example, by control measures. Stochastic models are required to examine this problem but current work in this area is very limited.The second area concerns immunity to parasitic infection. Few models take account of the substantive body of experimental work which attests to the significance of host responses (both specific and non-specific) to parasite invasion as determinants of parasite abundance within both an individual host and in the community at large. A start has been made in the investigation of models which mimic acquired immunity and immunological “memory” but much refinement and elaboration is needed (Anderson &; May, 1985a). In particular, the next generation of models should address the details of antibody-antigen and cell-antigen interactions in individual hosts as well as the broader questions concerning herd immunity. Heterogeneity in immunological responsiveness as a consequence of host nutritional status or genetic background must also be condsidered.The final topic is that of population genetics. Geneticists invariably consider changes in gene frequencies without reference to changes in parasite or host abundance, ecologists and epidemiologists have tended to study changes in abundance without reference to changes in genetic structure while immunologists have focused on the mechanisms of resistance to parasitic infection without reference to population or genetic changes. It is becoming increasingly apparent that host genetic background and genetic heterogeneity within parasite populations (e.g. the malarial parasites of man) are important determinants of observed population events (Medley &; Anderson, 1985). Future research must attempt to meld the areas of genetics, population dynamics and immunology. Such an integration presents a fascinating challenge.