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At the end of their report on the historic advances of mathematical epidemiology in this century, Anderson and May (1991) conclude: "Surprisingly, however, despite the current sophistication of this literature, the insights gained from theoretical work have, in general, had little impact on empirical approaches to epidemiological study and the design of public health policy". In part they attribute this to the abstractly mathematical nature of this literature. Another part of the explanation, which I want to address here, is the different terminology used by mathematical and empirical/medical epidemiologists. Even the meaning of 'epidemiology' strongly depends on the discipline. A classical medical epidemiologist studies the distribution and frequencies of infection and disease on the population level. The aim is to identify the factors responsible for the observed patterns, to make predictions and develop vaccination programs. According to the types of studies used descriptive, analytic and experimental epidemiology can be distinguished (see medical dictionaries). The mathematical approach is missing. A theoretician may view modern epidemiology as the medical discipline concerned with the consequences of host-parasite interactions for the population dynamics of both, parasites and hosts (parasites in a broad sense, see e.g. Anderson & May, 1991). Others will rather term this ecological epidemiology (Scott & Smith, 1994) and think of it as a specialization. A biologist may see epidemiology as the part of parasite population biology mainly studying infections of humans and managed farm animals (e.g. Grenfell, Dietz & Roberts, 1995). The way of thinking, the theories referred to and the terminology used will very much depend on the background, as does the selection of journals consulted.
More recently, the growing knowledge in parasitology, immunology, cell and molecular biology has improved our understanding of the infection and immune status of individuals. Together with newly-developed techniques these advances help in the quantification of patterns of infection and immunity at the population level. This has generated a new epidemiological discipline, which studies the influence of innate and acquired population immunity on epidemiological processes and is concerned with epidemiological surveillance. If the immune status of the population is assessed regularly, this allows the estimation of the importance of diseases and the planning and evaluating of vaccination programs (after Zetkin & Schaldach, 1992). What to call this new field? The expression immunoepidemiology, to my knowledge, arose and is explicitly used mainly in the context of helminth infections, often in combination with a mathematical model (see e.g. Anderson & May, 1985; Quinell & Keymer, 1990; Woolhouse, 1992; Grenfell et al., 1995). I cannot always agree with its use; either because the transfer of results from the individual to the population level is missing (see e.g. Schweitzer & Anderson, 1991; MacDonald et al., 1994; Jenkins & Wakelin, 1994) or because the relation to immunological parameters is not obvious (Bundy, Grenfell & Rajagopalan, 1991; Bundy, 1994). The empirical side seems to refer to the same field as seroepidemiology. When titles of research articles and their key words are considered this latter expression is much more widely used then the former.
Against my better judgement, the following short review focusses on theoretical approaches to the immunoepidemiology of different diseases. It is meant to highlight their contributions to current topics in the field and to show where and how mathematics can help. I will also point out open questions and methodological problems which can arise from the dependence of immunoepidemiology on research in other fields.
(Immuno)-epidemiological field studies have provided quantitative information on the relationships between parasite loads, immune responses, host age and sex/gender (e.g. Haswell Elkins et al., 1992; Tolle et al., 1993; Vlassoff & Bonilla, 1994.; Quinnell et al. , 1996; van Dam et al., 1996.) and on the efficacy of vaccination efforts (Bolotovskii,et al., 1990). In many cases the observed patterns have proven to be difficult to interpret because of the underlying biological interactions and their ecological and genetical aspects and implications. These include the influences of the biological and social environment (e.g. Becker, Bahrampour & Dietz, 1995), and of the co-evolutionary history of parasites and their hosts (e.g. Ewald, 1994; Gupta & Hill, 1995). Furthermore, many results from field studies are unfortunarely only correlative. It also means that one should not be too surprised to find a lot of variability and heterogeneity in traits of the parasites (e.g. virulence, immunogenicity or transmissability) as well as in those of the hosts (e.g. innate and acquired immunity or development of disease). As proposed by Anderson and May (1991) one way of partly resolving or directly addressing these difficulties is to resort to simple mathematical models.
It is, for instance, unclear whether the rise of worm burdens in older children and their decline in adults reflects age-related changes in exposure or resistence to infection in older age groups. Woolhouse (1992) used a mathematical model to explore the expected patterns of age-related variation in parasite burdens and the correlation between parasite burdens and immune responses in helminth infections. His models generated some complex and counter-intuitive patterns which challenge our understanding of protective immunity. The results imply that previous data analyses may have been too simplistic.
Aggregated frequency distributions in human infections, especially characteristic for macroparasites, may be the result of behavioural influences on exposure (to parasites or vectors) or of factors affecting parasites after infection, such as immune responses. To exclude the first source, one would have to show that variation in the level of infection is independent of the degree of exposure. Theoretical work has dealt with both the sources and impact of parasite aggregation without giving definite answers. A recent approach using Moment Closure Equations (Grenfell, Dietz & Roberts, 1995) related mean parasite load to aggregation (described by the negative binomial) and discussed the degree of heterogeneity in immunity which had to be assumed in the model to generate the observed age-related patterns.
In vitro studies have convincingly demonstrated the blocking activity of specific antibody responses to human helminth infection. How important are these in the field situation? Several findings have been taken as epidemiological evidence for blocking activities: (a) positive correlations between antibody levels and the rate of reinfection with schistosomiases after chemotherapy, (b) peak levels of antibody in younger, more susceptible individuals and (c) lower ratios of blocking antibodies to other antibodies in older, less susceptible age groups. Woolhouse (1994a) employed a mathematical model to explore expected age-specific relations between antibody levels, parasite burdens and reinfection rates for different combinations of protective, neutral and blocking immune responses. His models can generate the above patterns without invoking blocking activity, especially if the different antibody responses persist for different periods of time in the absence of antigen (immunological memory). Thus, none of the patterns cited in favour of blocking activity offers unambiguous evidence for its importance at the population level.
Immune responses to malaria have been shown to be species-, serotype- and stage-specific, but the importance of specific antigens in protective immunity remains unclear (e.g. Day & Marsh, 1991). Gupta & Day (1994) tried to clarify the relative contributions of conserved and strain-specific immune responses in protection against malaria. According to their results, the observed patterns of age-prevalence are best explained by assuming a protection threshold against infection for the conserved immune responses and a linearly exposure-dependent 'anti-disease' immunity. These theoretical findings are compatible with a parasite population consisting of several independently transmitted strains each conferring some degree of 'anti-disease' immunity, but not protecting against reinfection by the same strain.
The presence of antibody reduces vaccine efficacy. In diseases against which maternal antibodies play a role, the optimum age for vaccination depends on the rate of the decline of this maternal protection. In measles, maternal antibodies decline exponentially with a delay of 2-4 months and a half-life of 1-2 months. Williams, Cutts & Dye (1995) used this result in a mathematical model and calculated 11-19 months as the optimal age range for a single dose of vaccine to children. In addition, if this optimal range cannot be met for some reason, it is better to postpone than to advance the vaccination.
Data concerning the effects of the use of insecticide-treated bed nets on exposure to malaria are ambiguous. Snow et al. (1996) employed a constant risk catalytic conversion model to estimate the force of infection in communities with and without insecticide-treated bed nets. It was based on a survey among infants and used presence of Plasmodium falciparum parasites and total P. falciparum Immunoglobulin M (IgM) seropositivity, both independently and in combination. The results demonstrated a significant reduction by 50% in parasite prevalence, IgM seropositivity, and the force of transmission. Due to bed net use more 'treated' infants entered their second year of life without having been exposed to P. falciparum than control infants. As this delays their acquisition of effective immunity, the effects of this delay will have to be carefully monitored during future vector control programs.
One of the major open questions concerns the relationship or distinction between infection and disease. Studies on infections with intestinal helminths, for instance, suggest that our perception of pathology might be too narrow (Bundy, 1994). Moderate intensities of infection have been shown to affect the physical development of children, an effect which seems to be reversible by anthelmintic therapy. From animal studies, we know that almost anything that is important in their lives correlates with size and that there are trade-offs between investing in immunity and growth or reproduction (Zuk et al. 1996, Parasitology Today; Oppliger, Christe, Richner, 1996). What are the consequences at the population level of ignoring the stunting effects of moderate worm burdens on individuals?
A partialy related problem is that data collection even in large surveys is often designed for a specific purpose but that the same data has to also be used to address other questions. In clinical surveys, for instance, the assessment of morbidity is often an inadequately-designed secondary problem. This casts doubts on the reliability of conclusions about morbidity drawn from these data. On the other hand, it strongly suggests careful thinking about who else might be interested in the data of a planned survey and to involve them in setting up the design.
Adequacy is also a problem when results from in vitro experiments or studies on animal models are extrapolated and used to explain immune resistance and immunopathology in humans (Butcher, 1996). Homogeneity and clonality which are advantageous when one wants to understand mechansims, e.g. on the molecular level, become problematic. As was shown in the example of blocking antibodies, epidemiological evidence is often correlative and so can lead to premature conclusions on the relevance of in vitro results, without looking for alternative explanations (Woolhouse, 1994).
Another difficulty is related to the occurence of multiple infections with different parasites of (closely) related or unrelated species. Do non-focal parasites interfere with the seroepidemiologic surveillance of the parasite infection of our interest (see e.g. Alarcon de Noya, et al., 1996)? More generally, confusion on which immunological markers best correlate with protection hinders the assessment of the immune status of a population.
In terms of population biology immuoepidemiology/ seroepidemiology investigates the consequences of host immunity for the population dynamics of the parasite. In doing so, it reduces the intimately coupled host-parasite dynamics to a one-way relationship. There are many situations where this reduction just means simplification without doing too much harm, but there are definitely also contexts, e.g. when thinking of vaccination strategies, where the feedback nature of the relationship has to be taken into account.
The work summarized above clearly shows how the mathematical approach can contribute to quantifying and understanding patterns of infection and immunity at the population level. Some of the problems listed above could also be addressed by mathematical models, e.g. the effects of introducing heterogeneity into lab settings or of stunting of linear growth in wormy children. Of course, the best thing would be a combined effort of theoreticians and empirists. Bringing me back to the point I made in the introduction, this means that immunoepidemiologists have to take their theory to the field (see Woolhouse, 1994b) and carefully explain the implications of their results to seroepidemiologists. These in turn have to convince their colleagues in the lab to design experiments which are easier to relate to the situation in the field.
Acknowledgement
I thank Kirsten-Andre Senti, and Paul Ward for discussions and comments on an earlier version of this manuscript.
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Denis Mollison, 19th March 1997