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15 Expenmental Control of Malaria in West Africa Epidemiology encompasses a sophisticated field of ecological knowl- edge, and complex mathematical models are available to describe and predict patterns of disease incidence in space and time. The Garki project in Nigeria began in 1970 to provide detailed information on all factors in the transmission of malaria and to test hypotheses about the dynamics of malaria. The project was based on epidemiological models of proven value, it was carefully planned, and it had appropriate controls. It was viewed as a prototype for more extensive malaria control projects else- where in Africa. Although the project was carefully designed and executed in an inte- grated way over several years and data were gathered on the basis of a realistic mathematical model of malaria transmission, it failed to produce the predicted results, because incorrect assumptions were made about the biology of the mosquito vectors. In particular, it was assumed that all mosquitoes behave alike, whereas resting behavior actually varied in such a way that a large fraction of the mosquitoes did not land inside buildings, where they would have been exposed to the contact insecticide used. This case study highlights the importance of accurate and detailed natural his- tory in the design of effective control strategies and the effect of initial assumptions on the results of using even sophisticated models. 190

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Case Stucly ROBERT M. MAY, Department of Biology, Princeton University INTRODUCTION Malaria might well be the most important public health problem in tropical Africa. The intensity of malaria transmission is so high that control is very difficult, and many malariologists have suggested that humans should not interfere with the established natural immunity in the popu- lation, inasmuch as intervention could increase the severity of the clinical manifestations of malaria and the mortality caused by it in older children and adults. Largely for that reason- and because the public health infra- structure was inadequate theory predicted that available programs to control malaria would not work, and Africa was not included in the global malaria eradication program launched by the World Health Organization (WHO) in the 1950s. However, spraying houses with DDT was locally effective in inter- rupting malaria transmission, and the results of later pilot projects in various African countries suggested that malaria transmission could be interrupted, particularly in forested areas, if insecticide coverage were total and were followed by full surveillance. But in none of these pilot projects were quantitative epidemiological data collected. In view of this background, WHO decided to begin a field research project, carefully designed to provide information on all the factors involved in malaria maintenance and transmission. The northern part of Nigeria, specifically the Garki district, was selected for this project. The designers of the project decided to put more resources than usual into collection of baseline data and into evaluation of the impact of spraying houses with an effective residual insecticide (either alone or in combination with mass administration of drugs). As part of this effort to understand the dynamics of malaria transmission, a mathematical model was devel- oped and tested against data. The model was developed in an attempt to simulate malaria transmission realistically, in the hopes of understanding the various factors involved and improving the planning of control pro- grams. The Garki project was also designed to study an array of seroim- munological tests administered before, during, and after the application of control measures. The project is described in detail in The Garki Project, edited by Mol- ineaux and Gramiccia (19801. 191

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192 SELECTED CASE STUDIES THE ENVIRONMENTAL PROBLEMS Malaria is caused by the multiplication of parasitic protozoa of the family Plasmodiidae in the blood cells or other tissues of the vertebrate host; the clinical symptoms in humans arise from multiplication of the blood stages of the parasite. The several genera of malarial parasites are associated with different hosts. Four main species of Plasmodium are found in humans: P. falciparum, P. vivax, P. malariae, and P. ovale (comparatively rare); P. falciparum is the most common in tropical regions and is of greatest concern in the Garki region. and P. vivax is most common in temperate zones. Infection of a human host begins with the bite of a female anopheline mosquito and the injection of sporozoite stages of the parasite into the blood- stream. These stages are carried to the liver, where they develop in the parenchymal cells. After an incubation period of several days (or months, as some researchers have argued for P. vivax), these exoery~rocytic stages (i.e., from outside the red cells) grow, divide, and release merozoites into the bloodstream. The merozoites penetrate red cells, where they grow and subdivide to produce more merozoites, which rupture the host cells and invade other red cells. At some ill-understood point in this process, some of the merozoites develop into sexual stages, the gametocytes. Only the ga- metocytes are infective to the mosquito. When a vector mosquito bites a human and ingests male and female gametocytes, these are freed from the ingested blood cell, and the female gamete is fertilized and develops into an oocyst on the wall of the mosquito's gut. After about 10 days (the devel- opment time depends on temperature), immature sporozoites migrate from the ruptured oocyst to the mosquito's salivary glands and mature to infectivity, and the cycle is ready to repeat itself. Thus, the overall cycle of the malaria parasite involves transmission both from mosquito to human and from human to mosquito. One method of control or eradication of malaria, therefore, is to reduce the mosquito population sufficiently to keep the parasite cycle from maintaining itself. After World War II, DDT was effective in reducing mosquito populations and the incidence of malaria in many parts of the world (more in Asia than in Africa, where transmission rates have always been very high). The pesticide chosen in the Garki project was propoxur, which is more specifically targeted against anopheline mosquitoes than are broad-spec- trum insecticides, such as DDT. Malaria is commonly believed to be responsible for more deaths than any other infectious disease, both today and throughout history. It is listed as the principal cause of morbidity and mortality by most African countries (notably by Nigeria, the most populous). In Latin America, respiratory

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EXPERIMENTAL CONTROL OF MAI~RIA IN WEST AFRICA 193 tract infection tends to be listed as the most common cause of morbidity and mortality, followed by malaria and then measles; malaria ranks first in Brazil and Colombia. In Asia, gastrointestinal infection is the most common, followed by respiratory infection, with malaria ranking third as a source of morbidity; malaria ranks first in Malaysia. In short, malaria is a very serious public health problem throughout the tropical world (which is largely coincident with the developing world), and it is of especial importance in tropical Africa. GENERAL APPROACH The general approach of the Garki project was formulated on the basis of earlier pilot studies in Africa and elsewhere, all of which were quali- tative, rather than quantitative. In contrast with the earlier studies, the Garki project had clearly formulated quantitative objectives. The main objectives were as follows (Molineaux and Gramiccia, 1980, p. 211: "To study the epidemiology of malaria in the lowland rural Sudan savanna. This means in particular a concentration of the study on the measurement of entomological, parasitological and seroimmunological variables and on their relationships. Also included were some meteoro- logical, demographic and clinical variables, and the study of the prevalence of abnormal haemoglobins in the population." To measure the effect of specified activities directed toward inter- rupting transmission. Such intervention included spraying with a residual insecticide, propoxur, alone and in combination with mass administration of drugs. To undertake control measures in conjunction with the construction and testing of a mathematical model of malaria transmission. The general aim was to develop such a model into a planning tool that permitted comparison of the expected effects of different control strategies. Specif- ically, the model was developed to link entomological variables with parasitological variables (particularly the prevalence and transmissibility of P. falciparum) and to calculate the expected parasitological effect of defined changes in mosquito population density. The model also sought to permit evaluation of the effects of specific schemes for the mass ad- ministration of drugs, including the estimated role of immunity. DEVELOPMENT OF THE PROJECT Boundaries In the preparatory phase, from September 1969 through September 1970, preliminary entomological and parasitological surveys were made,

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194 SELECTED CASE STUDIES and specific areas and clusters of villages were chosen for detailed study. Protocols, forms, and operation manuals were drafted, and field and lab- oratory methods were tested. The boundaries of the study were, in effect, defined as specific villages in the Garki region. Study Strategy anal Monitoring Drawing on experience gained in earlier, qualitative pilot projects in Africa and elsewhere, the designers of the Garki project produced a study strategy that divided the operation into three main phases of data collection and monitoring. In the baseline phase, from October 1970 through March 1972 (which included a dry season, a wet season, and a second dry season), baseline epidemiological and parasitological data were collected in the clusters of villages that had been selected for followup. The preliminary insecticide and drug trials were also run. In the intervention phase, from April 1972 through October 1973 (which included a wet season, a dry season, and a second wet season), the intervention strategies and the monitoring of epidemiological variables in the treated and untreated clusters of villages were implemented. The length of this phase of the project was not fixed in advance, but rather was left open to be guided by accumulated knowledge. In February 1972, a review of the results obtained up to then suggested that the additional information likely to be gained from a third year of intervention and monitoring would not justify the expense and the expected additional loss of population immunity (as discussed in the introduction of this case study). In the postintervention phase, from November 1973 to the termination of the project in February 1976, selective administration of drugs in the villages covered during the intervention phase was continued, as was epidemiological monitoring in the villages treated with the most intensive strategies and in one cluster of untreated (control) villages. The antimosquito insecticide propoxur was sprayed, primarily inside buildings, in 164 villages, distributed over roughly 1,000 km2 a total of around 30,000 huts that housed a total population of some 50,000 persons. Propoxur is a contact chemical, so a mosquito must land on a sprayed surface if it is to pick up the insecticide. It remains active against mosquitoes on sprayed surfaces long after application. The coverage with insecticide, expressed as a proportion of huts sprayed, averaged about 99%. This coverage was estimated immediately after each spraying; the true coverage must have been somewhat lower, owing to building and repair activities between rounds of insecticide application. A combination of the antimalarial drugs sulfalene and pyrimethamine

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EXPERIMENTAL CONTROL OF MALARIA IN WEST AFRICA 195 was given to about 16,000 people in 60 of the sprayed villages. Infants were excluded, but visitors were included. The proportion of the total population given the drugs averaged about 85~o (higher in the wet season, lower in the dry season). USES OF KNOWLEDGE The relevant ecological facts pertaining to the dynamics of malaria transmission are conveniently discussed under two headings: the mosquito and the malaria parasite. Human immunology, although extensively stud- ied (Molineaux and Gramiccia, 1980), did not yield any findings partic- ularly relevant to the overall design of control programs and is not treated here. The Mosquito The extent of contact between mosquitoes and humans in the Sudan savanna is very high indeed: the biting rates of Anopheles gambiae sensu lato and A. funestus were found to attain seasonal peaks of 174 and 94 bites per person per night, respectively (in studies that averaged more than 8 nights). The vectorial capacity, defined as the rate of contact between human hosts via the mosquito vectors, reached a seasonal peak of about 40, which is some 2,000 times the critical value for maintaining endemic malaria. The cumulative inoculation rate by mosquitoes reached a max- imum of 145 sporozoite-positive bites per person in l year (of which 132 were in the wet season). The mosquito density, and hence the extent of malaria transmission, in the Sudan savanna varies widely with season, year, and locale, according to Molineaux and Gramiccia (1980), who write: In most villages, the vectorial capacity drops below its critical level for about half of the year (this does not necessarily prevent transmission, given the large reservoir of parasites), while in some it remains well above the critical level throughout the year. The variations from year to year are relatively important; over a period of 3 years, these variations followed the variations in total rainfall in the case of A. funestus but not in the case of A. gambiae s.l. Villages, even when not obviously different on inspection and located only a few kilometres apart, differ in vector density, anopheline fauna (A. funestus has a very uneven distribution) and probably in vector behaviour and karyotypes. Among 8 villages, the cumulative inoculation rate ranged from 18 to 145 sporozoite-positive bites in one year. The local and yearly variations stress the need for adequate baseline and comparison (control) data for a correct evaluation of the impact of control measures.

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196 SELECTED CASE STUDIES The Malaria Parasite In general, the baseline prevalence of malaria parasitemia was high, and the age-specific curves of both prevalence and density of infection were typical of a high rate of transmission with a high level of acquired immunity. The findings were the same on each of the three parasites (P. falciparum, P. malariae, and P. ovate). There was relatively little variation among villages or between years. The rate at which infants acquired malaria and the rate of onset of episodes of patent parasitemia (with fever, etc.) in the general population both testified to the high rate of transmission. The marked increase in the rate at which patent parasitemia disappeared with increasing age and the high ratio (nearly 1:1) of the entomological inoculation rate to the infant conversion rate (the ineffectiveness of sporozoite-positive bites) confirmed the high level of population immunity. The combination of propoxur spraying and mass administration of sul- falene and pyrimethamine every 10 weeks reduced the prevalence of P. falciparum to a very low point in the dry season, but it did not significantly interrupt malaria transmission. Nor did it prevent an increase in prevalence in the wet season, when natural conditions favored mosquito breeding. A new equilibrium, with incidence oscillating between wet and dry seasons, was reached rapidly, and continuation of the intervention program would probably not have affected this result significantly. It was concluded that mobility of the human population, which was relatively pronounced, was unlikely to be the main cause of the maintenance of transmission. As discussed at length below, the main limiting factor was probably the exophily of some of the mosquitoes i.e., their preference for resting outdoors. When propoxur was sprayed and drugs administered more often (every 2 weeks in the wet season, every 10 weeks in the dry season), the prev- alence of P. falciparum decreased to around 1% in the dry season and to 5% or less in the wet season. But transmission was still not interrupted greatly. As with the lower-frequency intervention, a new oscillating equi- librium was fairly rapidly attained, and it seems unlikely that continuation of the intervention would have modified the result. Again, it was concluded that exophily of the mosquitoes was the main cause, rather than population mobility. As expected, mass application of the drugs at high frequencies for 1.5 years caused a temporary loss of immunity against P. falciparum, which was reflected in the resurgence of malaria in the postintervention phase of the project.

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EXPERIMENTAL CONTROL OF MAI~RIA IN WEST AFRICA GENERAL THEORY 197 The basic model for malaria was first set out by Ross (1911, 1916) and later refined by MacDonald (1952, 1957, 1973), who included the latent, infected-but-not-yet-infectious period for the mosquito. If we divide the human host population into those who are susceptible and those who are infected and divide the female mosquito population into the susceptible and the infected, we can construct a pair of differential equations to describe the essentials of the dynamics of infection. dxldt = (abMlN)y(1 -x)-rx, dyldt = ax(1 - y)- by, where (1) (2) x 1S y 1S N is M is the proportion of the human population infected, the proportion of the female mosquito population the size of the human population, the size of the female mosquito population, a is the rate of biting on a human by a single mosquito (number of bites per unit time), b is the proportion of infected bites on humans that produce an infection, r is the per capita rate of recovery for humans (fir is the average duration of infection in a human host), and is the per capita mortality rate for female mosquitoes (lid is the average lifetime of a mosquito). infected. In this simplest model, the total populations of both humans and female mosquitoes are assumed to be unchanging (N and M constant), so the dynamic variables are the proportions infected in the two populations (x and y). Equation 1 describes changes in the proportion of humans infected. New infections are acquired at a rate that depends on the number of mosquito bites per person per unit time (aMlN), on the probabilities that the biting mosquito is infected (y) and that a bitten human is not already infected (1 -x), and on the chance that an uninfected person bitten by an infected mosquito will become infected (b); and infections are lost by the return of infected people to the uninfected class, at a characteristic recovery rate (rx). Equation 2 describes changes in the proportion of mosquitoes infected. The gain term is proportional to the number of bites per mosquito per unit time (a) and to the probabilities that the biting mosquito is uninfected (1 - y) and that the bitten human is infected already (x); the loss term arises from the death of infected mosquitoes (y).

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198 SELECTED CASE STUDIES More formally, the loss terms for infected humans and for infected mos- quitoes both involve death and recovery. But for human hosts the recovery rate is typically greater than the death rate (by 1-2 orders of magnitude), whereas for mosquitoes the opposite is typically the case; the above for- mulation is therefore a sensible approximation. This model is, of course, highly simplified. One of its glaring flaws is the failure to disarticulate the "infected" categories of human and mosquito hosts to take account of the various developmental stages of the parasite. For instance, the model does not incorporate the incubation period of Me parasite in the mosquito (during which no sporozoites are present in Me salivary glands of the "infected" mosquitoes), even though this incubation period is comparable with the mean life span of the mosquito. We pursue this complication below. Likewise, the model does not distinguish between the pathological asexual merozoite blood stages and the infectious gametocyte sexual stages in the human. Encounters between biting mosquitoes and the humans they bite are assumed to be random. Notwithstanding those shortcomings, the simple model defined by Equations 1 and 2 is useful in laying bare the essentials of the transmission process and in elucidating patterns in the diverse array of epidemiological data on different geographical regions. In particular, the model makes plain the significance of the "basic reproductive rate" of the parasite, in this context conventionally called z0 (MacDonald, 1952, 19571. The basic reproductive rate is essentially the number of secondary infections gen- erated by one infected individual in a population of susceptibles. If this number is, on the average, less than unity, the disease will be unable to maintain itself; if it equals or exceeds unity, the disease will be able to maintain itself. In general, the larger the basic reproductive rate, the greater the resistance of the disease to eradication. In this simple model, z0 = ma2bl,ur, . where m Is the number of female mosquitoes per human host (MIN). This result is intuitively understandable: the mosquito biting rate, a, enters twice in the cycle (hence, ah; transmission is helped by large numbers of mosquitoes per human host (large m) and by large b; and transmission is hindered by a high mosquito death rate or by fast recovery (large ,u and r, respectively). To be more accurate, we should recognize that a latent period of duration T must elapse before an infected mosquito becomes infectious. This in- troduces an additional factor, exp(- of), into Equation 3 to represent the probability that an infected mosquito will survive the latent period to (3)

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EXPERIMENTAL CONTROL OF MALARIA IN WEST AFRICA 199 become a transmitter of infection. The resulting expression for z0 (as first derived by MacDonald, 1952, 1957) is then z0 = ma2b expt-~T)I~r. A SPECIFIC MODEL (4) Dietz et al. (1974) developed a more realistic modification of the above model, which is presented in detail in Molineaux and Gramiccia (1980, Ch. 101. The essentials of the model are indicated schematically in Figure 1. There are two classes of people: one class has a low rate of recovery from malana, and all infections can be detected; the other class has a high recovery rate, and infections have only a 70% chance of being detected (owing to the low densities of parasites). Members of both classes re- peatedly are exposed, become infected, and recover, remaining within their own class except for a fixed rate of transition from the relatively susceptible class to the relatively immune class (the transition rate is determined by fitting the model to the data). The model thus takes into account the basic characteristics of immunity to malaria. Within the framework of this model, it is possible to calculate the prevalence of P. falciparum as a function of the vectorial capacity and of its spontaneous and man-induced changes. It is also possible to calculate the effect of mass administration of drugs on the prevalence of malaria. The model gave a good account of the basic dynamics of the interactions among humans, mosquitoes, and malaria. But the effects of insecticide ~ 1 NONINFECTIOUS NEGATIVE l l l l I I SLOW RECOVERY X3 ~X4 Y3 I ~NON I N F ECTI OUS FAST RECOVERY . FIGURE 1 Schematic illustration of malaria model of Dietz et al. (1974~. As dis- cussed more fully in text, diagram shows various categories of individuals considered in model and possible transitions between categories.

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200 SELECTED CASE STUDIES on mosquito longevity were not accurately estimated by treating the mos- quito population as homogeneous and as all resting indoors. Accurate prediction of the effects of insecticide on mosquito mortality, and on overall transmission dynamics, required an appreciation of the heteroge- neity of the environment, which was not built into the original model. The study concluded that the specific model described above does indeed simulate the epidemiology of P. falciparum infections with acceptable realism and that it can be used both for planning malaria control and for teaching the epidemiology and control of malaria. But important compli- cations enter into the estimation of the parameters in the model, particularly the estimation of the effects of insecticides on mosquito mortality rates. These complications in many ways constitute the most interesting of the lessons learned in this case. CONCLUSION: THE CASE STUDY AND ECOLOGICAL KNOWLEDGE It will be seen that the Dietz et al. model does not discriminate among different classes of mosquito vectors. A substantial complication, how- ever, arises from inhomogeneities in the effects of insecticides. In the Garki project, an insecticide was applied to interior surfaces of houses and was therefore more effective against mosquitoes that rest indoors after a blood meal. If insecticides do not affect all mosquitoes equally, mea- surements of the average biting rate and of average longevity might be severely distorted (Molineaux et al., 19791. Suppose that after spraying there are in effect two mosquito populations: a minority (initially pi = 0.2) that rest outdoors (exophilous) and are consequently relatively un- affected by the spraying, and a majority (initially P2 = 0.8) that rest indoors (endophilous) and suffer greater mortality. Let al = 1 bite per day and act = 0.05 per day for the exophilic mosquitoes, and a2 = 2 and ~2 = 0.5 for the endophilic ones. Let the latent period, T. equal 10 days for all mosquitoes. The correct way to calculate the effective index, a expt-/, which determines the transmission rate from infected mosquitoes to human hosts and is therefore relevant to evaluating the effects of intervention, is to take the appropriate arithmetic average of the separate indexes: peat exp(- ~l~l,u~ + p2a2 expf-~2T)/112 = 2.5. But if the endophilic and exophilic categories are not properly distin- guished, then the above index is likely to be estimated with average values of a and of ,u: a expt-,ul~l,u = 0.073 (where a = plan + p2a2 = 1.8

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EXPERIMENTAL CONTROL OF MALARIA IN WEST AFRICA 201 and ~ = Pled + P2~2 = 0 41) Molineaux et al. (1979) analyzed the consequences of this aggregation phenomenon in considerable detail and emphasized that aggregating the groups will always underestimate the biting capacity of the mosquito population and hence will always under- estimate the basic reproductive rate, zO, and overestimate the impact of insecticides. As the above example makes clear, these incorrect estimates can lead to seriously wrong conclusions. The above discussion captures the essentials of the most important surprise found in the Garki project. It was known from the outset that the intensity of transmission of malaria in these parts of Africa was very high. Indeed, the study showed the basic reproductive rate of the infection to be about 1,000; in other words, the transmission rate, or "vectorial ca- pacity of the mosquito," was about 1,000 times the critical value required for the maintenance of endemic malaria. This very high transmission rate put malaria in tropical Africa in a category of its own and constituted one reason that a control program like that tried in the Garki project was not attempted earlier. Against this background, however, it was not understood that heterogeneities in the environmental setting of the mosquitoes might invalidate simple estimates of the efficacy of insecticide application, which were based on assumptions that the mosquito population was effectively homogeneous and that most mosquitoes rested indoors much of the time. Thus, it was found that spraying with the residual insecticide propoxur did not have the expected effect on the prevalence of malaria, although coverage was as nearly complete as possible and the insecticide was very effective against the mosquito vectors (it produced a high mortality rate even at the beginning of the third wet season after the last application). Immigration of vectors or humans from unsprayed villages did not appear to be a significant factor. The decisive factor appears to have been the exophily of a substantial fraction of the mosquito vectors. The combination of exophily with a high biting rate maintained a high transmission rate. Thus, although the insecticide program was supplemented by administra- tion of drugs at high frequency and with high coverage and it reduced malaria to a very low incidence, it failed to interrupt transmission. In more detail, it was found that the effect of residual spraying in reducing A. gambiae s.l. populations, and hence malaria transmission, varied significantly among villages. The variation was probably related not to variations in spraying coverage or to distance from unsprayed villages, but to variation in the amount of exophily. The amount of ex- ophily appeared to be a relatively stable characteristic of particular villages, and it also appeared to be associated with genetic differences within species of the A. gambiae complex. The vector population attached to a village

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202 SELECTED CASE STUDIES appeared to be relatively isolated genetically most of the time. This was also in accord with the observation that the effect of spraying was influ- enced little by the size of the sprayed area. As to the possible genetic mechanisms underlying the behavioral dif- ferences between endophilic and exophilic mosquitoes, Molineaux and Gramiccia (1980) stated: A. gambiae s.l. in the study area is composed of A. gambiae s.s. and A. arabiensis. The dominant species is usually A. arabiensis but the relative abundance of the 2 species varies between times and places in ways which are not explained. A. gambiae s.s. is the more anthropophilic and has higher sporozoite rates; no clear-cut difference was demonstrated regarding exophily or effectiveness of propoxur. The vectorial capacity was estimated as if A. gambiae s.l. were a single species; appropriate sim- ulations show that this is unlikely to have introduced a large error in the estimate. The cytogenetic investigations of Coluzzi suggest that resting behaviour and exposure to propoxur are related less to the relative abundance of the 2 species than to the intraspecific frequency of certain chromosomal inversions, some of which may be associated with a relatively stable behaviour pattern of the individual. In short, the essential conclusion of the Garki study, which was not anticipated in the early planning, was that, if the resting behavior of a mosquito species is genetically determined, exophily will be a stable characteristic of individual vectors, and the usual method of interpreting the impact of residual insecticides on longevity, which tacitly assumes uniform bet haviour, is overoptimistic. From the parasitological point of view, the study was interesting, in that its longitudinal nature permitted it to demonstrate that almost everyone was infected early in life, not only by P. falciparum, but very probably also by P. malariae and even by P. ovale, which is commonly regarded as a "rare" parasite. In addition, early demonstration of the effect of parasitism on immunity confirmed that a degree of immunity is evoked by malarial infection and that continual reinfection is necessary to maintain such immunity over the long term. Other clinical studies showed inter- esting relationships between body temperature and parasitemia and showed a significant effect of malaria control on frequency of fever and on an- thropometric indicators of the nutritional status of children. In another conclusion, Molineaux and Gramiccia (1980) stated that "the new mathematical model, painstakingly tested against hard facts, allows much more realistic simulations of the epidemiology of malaria, both before and after the application of control measures, than was previously possible." Cohen and Singer (1979) developed the model further, incor- porating additional elements of realism (such as infection with more than

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EXPERIMENTAL CONTROL OF MALARIA IN WEST AFRICA 203 one species of malaria and a more accurate description of immune re sponses in human hosts) while retaining an essential understanding of the process of malaria transmission. REFERENCES Aron, J. L., and R. M. May. 1982. The population dynamics of malana. Pp. 139-179 in R. M. Anderson, ed. Population Dynamics of Infectious Diseases. Chapman and Hall, London. Cohen, J. E., and B. Singer. 1979. Malana in Nigeria: Constrained continuous-time Markov models for discrete-time longitudinal data on human mixed-species infections. Pp. 69- 133 in S. A. Levin, ed. Lectures on Mathematics in the Life Sciences. Vol. 12. Some Mathematical Questions in Biology. American Mathematical Society, Providence, R.I. Dietz, K., L. Molineaux, and A. Thomas. 1974. A malaria model tested in the African Savannah. Bull. WHO 50:347-357. MacDonald, G. 1952. The analysis of equilibrium in malana. Trop. Dis. Bull. 49:813- 828. MacDonald, G. 1957. The Epidemiology and Control of Malana. Oxford University Press, London. Macdonald, G. 1973. Dynamics of Tropical Diseases. Oxford University Press, London. Molineaux, L., and G. Gramiccia, eds. 1980. The Garki Project. World Health Organi- zation, Geneva. Molineaux, L., G. R. Shidrawi, J. L. Clarke, J. R. Boulzaguet, and T. S. Ashkar. 1979. Assessment of insecticidal impact on the malaria mosquito's vectorial capacity, from data on the man-biting rate and age-composition. Bull. WHO 57:265-274. Ross, R. 1911. The Prevention of Malana. 2nd ed. Murray, London. Ross, R. 1916. An application of the theory of probabilities to the study of a priori pathometry. Proc. R. Soc. A 92:204-230. Committee Comment In general, the interactions between hosts and parasites are examples of prey-predator associations that have some simplifying features espe- cially for human host-parasite systems, in which the population size of the human host is usually determined by other factors and much infor- mation on transmission and maintenance of the parasite is often available. Many public health studies can be viewed as examples of the interaction of environmental problems (broadly defined) with ecological principles. The Garki project is notable in that it was very thoughtfully designed, was maintained in an integrated way over several years, and carefully interdigitated the data gathered with a relatively realistic mathematical model. Moreover, the mathematical model, based on hard data and tested against data gathered in the course of the study, could be thought of as a

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204 SELECTED CASE STUDIES paradigm for a prey-predator model. It was successful in explaining the patterns of prevalence before, during, and after the intervention program. Interestingly, during construction of the basic model, no thought had been given to the possible effects of genetic and behavioral heterogeneity in the vector mosquito population. Such effects turned out to be the most important factor working against control. That a large fraction of the mosquitoes were exophilic meant that simple preliminary estimates of the overall transmission rate and of the likely effect of insecticides were incorrect. This story illustrates the need for careful design in the gathering of data (and the extent to which a thoughtful mathematical model can guide the process) and shows that, no matter how carefully these things are thought through, unexpected complications are likely. Beyond these platitudes, the story also illustrates a specific theme found in much contemporary ecological theory. It seems increasingly likely that spatial heterogeneity, with different dynamic processes going on in separate patches, will be the most important factor in the overall persistence of many natural prey- predator or host-parasite associations (Hassell and May, 19851. The Garki project is certainly one example: behavioral heterogeneity in the mosquito population was, on the one hand, the most important factor in maintaining infection in the presence of an intervention program and, on the other hand, a factor not initially reckoned with (in a preliminary analysis drawn from the conventional traditions of ecological theory, which too often treat the world as homogeneous). Reference Hassell, M. P., and R. M. May. 1985. From individual behaviour to population dynamics. Pp. 3-32 in R. Sibly and R. Smith, eds. Behavioural Ecology. Blackwell, Oxford, Eng.