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    Figure 1.

    Decision tree pathways. na = not applicable.

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    Figure 2.

    Predicted age-prevalence and age-incidence curves by transmission intensities The reference scenario is the transmission intensity observed at Namawala, Tanzania divided by a factor 16. Low transmission = Namawala transmission divided by 64; high transmission = one-fourth of Namawala transmission; very high transmission = transmission observed at Namawala. a, age-prevalence curve of patent parasit-emia; b, age-incidence curve of uncomplicated episodes; c, age-incidence curve of severe episodes; d, age-incidence curve of mortality.

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    Figure 3.

    Infectivity of the human population. a, reference scenario; b, scenario assuming full treatment coverage.

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    Figure 4.

    Age-prevalence curves of parasitemia under different case management scenarios during a simulated 20-year follow-up period. ▪ = no treatment; ▵ = reference; ▴ = moderate coverage (first year of follow-up); * = complete coverage (first year of follow-up); ○ = complete coverage (10th year of follow-up); • = complete coverage (20th year of follow-up).

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    Figure 5.

    Age-prevalence curves of anemia (hemoglobin level < 8 g/dL) The reference scenario is the transmission intensity observed at Namawala, Tanzania divided by 16. Low transmission = Namawala transmission divided by 64; high transmission = one-fourth of Namawala transmission; very high transmission = transmission observed at Namawala.

  • View in gallery
    Figure 6.

    Age-incidence curves under different case management scenarios at different durations of simulation during a 20-year follow-up period. a–c, age-incidence of uncomplicated episodes; d–f, age-incidence of severe episodes; g–i, age-incidence of mortality.

  • View in gallery
    Figure 7.

    Direct costs in relation to transmission intensity. Upper line = undiscounted; lower line = discounted.

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    Figure 8.

    Effect of changing case management in different transmission settings. The status of the population at baseline was defined by simulating the reference health system for 90 years for each transmission intensity. The follow-up period then ran for 20 years with the chosen health system, and the results are the average for the 20 years. The incidence rates quickly settled to a new level. Because of the uncertainty in the rates of severe morbidity and mortality in adults, the predictions for only for children less than 10 years of age are shown. ▪ = no treatment; ▵ = reference case management; × = full coverage.

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AN APPROACH TO MODEL THE COSTS AND EFFECTS OF CASE MANAGEMENT OF PLASMODIUM FALCIPARUM MALARIA IN SUB-SAHARAN AFRICA

FABRIZIO TEDIOSISwiss Tropical Institute, Basel, Switzerland

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NICOLAS MAIRESwiss Tropical Institute, Basel, Switzerland

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THOMAS SMITHSwiss Tropical Institute, Basel, Switzerland

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GUY HUTTONSwiss Tropical Institute, Basel, Switzerland

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JÜRG UTZINGERSwiss Tropical Institute, Basel, Switzerland

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AMANDA ROSSSwiss Tropical Institute, Basel, Switzerland

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MARCEL TANNERSwiss Tropical Institute, Basel, Switzerland

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An important shortcoming of existing methods for estimating the cost-effectiveness of malaria control interventions is that the incidence of illness and transmission dynamics are assumed to be independent of the case management system. We have developed a model for case management and integrated it into a stochastic simulation of Plasmodium falciparum malaria dynamics. This allows us to predict the incidence of clinical episodes and of mortality while incorporating effects of case management on persistence of parasites and transmission. We make predictions for a range of different transmission intensities in sub-Saharan Africa and simulate a range of case management scenarios with different coverage rates. The model predicts that high treatment rates have a proportionately greater epidemiologic impact at low transmission levels. Further development is needed for models for health-seeking behavior and referral patterns. The current model is a first step towards useful predictions of the epidemiologic and economic consequences of introducing and/or scaling-up of malaria control interventions.

INTRODUCTION

Models for the cost-effectiveness of different disease control strategies generally, and malaria control interventions in particular, usually assume the incidence of illness and transmission dynamics to be independent of the prevailing case management system.1,2 Decision trees typically start with the observation of an illness episode and consider how the episode is managed subsequently, but do not consider whether management itself affects the incidence of the disease. With infectious diseases such as malaria, this approach ignores the feedback that may arise from an effective case management system, which in turn reduces the frequency of infection, and thus impacts transmission dynamics.

Models for nosocomial infections and those recently developed to simulate the severe acute respiratory syndrome epidemic3,4 provide examples of approaches in which the operation of the health system interacts in a dynamic fashion with the biology of the infecting organism. In these models, prompt treatment of infections reduces epidemic spread, and thus results in both reductions in the subsequent burden of disease and in the requirements for treatment of secondary cases.

When the infection has a long time course, which may encompass several illness episodes, treatment may also reduce the subsequent burden of disease independently of its effect on transmission. In malaria, untreated Plasmodium falciparum infections can persist for many months, during which clinical attacks recur at irregular intervals.5 One of the current mainstays of malaria control is access to early diagnosis and effective treatment.6 Prompt and effective treatment not only reduces the reservoir hosts who are infective to mosquitoes, but also prevents recurrences. Longitudinal studies of malaria in endemic populations frequently record declines in incidence over time. A major reason for this is likely to be that study participants receive more frequent treatment and this reduces the incidence of subsequent malaria fever attacks, irrespective of any effect on transmission. Conventional cost-effectiveness analysis of treatment does not consider these effects.

Malaria control interventions, such as source reduction by means of environmental management, increasing the coverage of insecticide-treated nets (ITNs), indoor residual spraying, and (potentially) the introduction of a malaria vaccine, modify the demands on the health system, and thus affect both immediate direct impact and longer-term indirect effects of case management. This applies even when the intervention, such as vaccination, does not directly modify case management. It follows that prediction of the impact of preventative and curative interventions against malaria must take into account these dynamic effects.

This report presents a first attempt to develop a dynamic model including case management of P. falciparum malaria in a typical setting of sub-Saharan Africa. It has been integrated into a model for the clinical epidemiology and natural history of P. falciparum malaria.7 We compare the outcomes of different case management regimens in settings of different transmission intensities.

MATERIALS AND METHODS

Epidemiologic model.

The epidemiologic model is a stochastic individual-based simulation of P. falciparum malaria in endemic settings that uses a five-day time step. The primary input is the pattern of the entomologic inoculation rate (EIR) in the absence of malaria control interventions, with separate values of the EIR specified for each of the 73 five-day periods during the year.7,8 For the present analyses, we simulate populations of 100,000 individuals, with an approximately stationary age distribution matching that of the demographic surveillance site in Kilombero, Tanzania in 1997–1999.9

For every individual in the simulated population, each discrete P. falciparum infection is characterized by a simulated duration and parasite density at each five-day time point.9 The host acquires immunity as a function of exposure and this in turn modifies the parasite density, and infectivity to mosquitoes10,11 at subsequent time-points. At each time point, a clinical event, either uncomplicated clinical malaria, severe malaria, or death from either malaria or other causes, may occur. Probabilities for occurrence of these events depend on the parasite density, recent exposure, and age-dependent co-morbidity. They have been determined by functions that have been fitted to field data across a wide range of transmission settings.1214 In addition, the prevalence of anemia (hemoglobin levels less than 8 g/dL) is assigned at the population rather than the individual level, as a function of simulated age and parasite prevalence.15

Clinical events.

There are five different entry points into the case management tree: no event, uncomplicated malaria, severe malaria, indirect malaria death, and non-malaria death or out-migration. They are defined as follows.

No event, includes asymptomatic malaria infections. In this case, the simulated individual continues to the next time point, with the natural history of P. falciparum infections unmodified by the case management model.

Uncomplicated clinical malaria comprises P. falciparum infections that may be treated either at home or in peripheral health facilities. The model assumes that the risk of uncomplicated clinical malaria depends on whether the parasite density exceeds a critical threshold, which in turn is a function of past exposure.13 The case management implications of uncomplicated clinical malaria further depend on whether the host has recently been treated for malaria. Two possibilities were considered, as follows. The first is uncomplicated clinical malaria in the absence of recent treatment. This is defined by no treatment over the previous 30 days (6 time points). The decision tree pathways for this scenario are shown in Figure 1a. They include entry into the formal health care system and receiving the first-line drug, self-treatment at home with the recommended first-line drug, or absence of seeking of malaria treatment. The second is an uncomplicated clinical malaria episode that occurs despite recent treatment history. Figure 1b shows the decision tree pathways for this scenario. An uncomplicated malaria case that was treated in the past 30 days is assumed to either seek care or not. If care is sought, it is assumed to take place in the formal health care system, with treatment being based on the second-line drug. We do not consider the possibility that patients self-treat after drug failure because this would very likely involve ineffective retreatment with the first-line drug, with no epidemiologic consequences.

Severe malaria episodes are those clinical malaria episodes that are life-threatening if they are left untreated. We consider these as equivalent to those events that would have led to an admission diagnosis of severe malaria, had the patient presented to a health facility.12 The current model assumes that a severe malaria case can either be treated as an in-patient or not be treated at all. In the former case it is assumed that compliance is 100%. There are three possible clinical outcomes for treatment of a severe malaria episode, namely, death, recovery with neurologic sequelae, or full recovery (Figure 1c).

Indirect malaria death considers those deaths that would not have occurred in the absence of prior malaria exposure but which do not meet the criteria for severe malaria.12

Non-malaria death and out-migration correspond to events that occur independently of the parasitologic status of the host. These events are simulated to maintain the correct age-structure of the simulated population.

When more than one simulated clinical attack occurs within 30 days of another attack, these are counted as the same episode. Thus, there can be several treatments for one episode. The severity assigned to the episode is assigned to that of the most severe malaria attack within the 30-day period.

Each decision tree pathway predicts the outcome in terms of whether the parasites are cleared, and the clinical outcome (i.e., death, recovery with long-term sequelae or full recovery). The epidemiologic effects of the case management depend stochastically on the values of the joint probabilities of the clinical and parasitologic outcomes, conditional on the clinical event. These conditional probabilities are computed by calculating the probabilities for each branch of the decision tree pathways (Figure 1). For the model of uncomplicated malaria, the probabilities associated with each branch in the decision tree were obtained from the literature (Table 1).

For the severe malaria model, we used in-patient case fatality rates, and Qh(a), from a recent study in Tanzania,16 estimated corresponding community case fatality rates, Qc(a). Qh(a) varies with age a, taking values from 3% to 13%. Qc(a) takes values estimated previously using our model for severe malaria and mortality assuming the two risks to be related via a constant odds ratio, φ1, taking a value of 2.09,12 i.e.,

Qc(a)=φ1Qh(a)1Qc(a)1Qh(a)

We assume negligible drug-resistance to quinine, so that parasites are cleared in all hospitalized cases who survive. We assign a probability of sequelae, Rx, with a value independent of treatment (Table 1).

Disability adjusted life-years (DALYs).

Years of life lived with disability are calculated using standard methods17 on the basis of the duration of disability, and respective disability weights (Table 2). These weights for different malaria-attributable disease conditions have been obtained from the Global Burden of Disease (GBD) study.18

Years of life lost (YLLs) and DALYs (age-weighted) are calculated assuming age-specific life expectancies based on the life-table from Butajira, Ethiopia, with an average life expectancy of 46.6 years at birth.19 This life-table represents that of an east African setting, but is characterized by low malaria transmission. For example, it is very similar to that for Hai district, a high-altitude site in Tanzania.20

In a first step, YLLs and DALYs are presented with no discounting. Subsequently we compare the results with those obtained using a 3% discount rate, which is the one most commonly used in cost-effectiveness analyses.1,2

Malaria transmission intensity.

The introduction of changes in case management (or of other interventions) leads to transient behavior, which may in principle modify the level of P. falciparum transmission. These effects on transmission are captured in the model by the effects on infectiousness of the human population resulting from clearing parasites. The simulation model predicts for time point t the proportion κ̄m(t) of vectors that become infected at each feed on a human host.10,11 We adjust this to give κu(t) = 0.56 κ̄m(t) to allow for the bias arising because κ̄m(t) is estimated from artificial feed data.10 We record the value κu(0)(t) that κu(t) takes in the simulation of the reference scenario to which a change in the case management model has been applied, and compare this value to κu(1)(t), the prediction of κu(t) for the same time-point in the simulation with a change in case management. The effect of the change in case management on transmission is then modeled by a change in the EIR in adults at lv time units later (Emax(t + lv)), such that

Emax(1)(t+lv)=Emax(0)(1+lv)κu(1)(t)κu(0)(t)

where lv corresponds to the duration of the sporogonic cycle in the vector, and where Emax0(t + lv)/κu(0)(t) is the overall vectorial capacity. The consequences for the infection rates follow from details of the epidemiologic model.8

We considered four different intensities of transmission, each with the same seasonal pattern as that in Namawala, Tanzania21 (Table 3). For the reference scenario, we used an overall annual EIR of 21 infectious bites per year, which represents a typical level of transmission for a meso-endemic setting.22,23

Health systems.

Uncomplicated malaria patients seeking formal health care in Tanzania are usually diagnosed during an out-patient visit either in a health center, a dispensary, or a hospital. A diagnostic test (normally light microscopy of finger prick blood smears) is performed on less than 10% of treated cases (National Malaria Control Program, 2004, unpublished data). Current Tanzanian national treatment guidelines recommend that an uncomplicated malaria episode be treated with sulfadoxine-pyrimethamine (SP) as the first-line drug. Amodiaquine serves as the second-line drug, and quinine is used for treatment of severe malaria.24 Our models assume that formal-sector treatment adheres to these practices (Tables 4 and 5). We also assume that SP is used as the drug of choice for self-treatment, but the efficacy is assumed lower to account for lower quality of drugs purchased in the private sector. The levels of compliance and of drug resistance that we assume are given in Table 1.

We evaluate the effects of different case management in our model by varying either malaria treatment seeking-behavior or availability of treatment. Table 3 summarizes the set of scenarios considered that include seven different sets of assumptions for the level of treatment.

No treatment.

In this model, we assume no access to anti-malarial treatments.

Reference case management.

In this model, we took the same probability of seeking treatment of uncomplicated malaria as in our recent simulation of a malaria vaccine trial,25 but assume 20% of treatments to be self-treatment and 80% to use formal care. We use a value of 48% for the probability of seeking treatment of severe malaria (Table 1).26,27 The treatment rates for uncomplicated episodes are low because the model for clinical episodes was fitted to very intensive surveillance data from Senegal, which included minor fevers that would be very unlikely to lead to treatment seeking.13 The treatment rates were estimated by triangulating the predictions of this model for clinical episodes with health system attendance data from Manhiça, Mozambique.25

Moderate coverage.

In this model, we use recent data from the Tanzanian National Malaria Control Program of the Ministry of Health.28 This report states that 27% of children less than five years of age were treated within 24 hours in health facilities, 13% at home, and 2% at traditional healers. The remaining 58% received no treatment within 24 hours from the onset of disease.29 We use these percentages of 27% of children receiving formal care, and 13% self-treatment of uncomplicated malaria episodes (Table 1). We use the same coverage of formal care for severe malaria as in the reference model. In the context of our five-day time-step, we do not distinguish in our simulations whether treatment is within 24 hours or not.

Abuja target coverage.

Sixty percent of uncomplicated episodes are treated with the appropriate drug. The simulated coverage of hospital treatment of severe episodes remains at 48%.

Complete coverage.

We assume that 100% of uncomplicated clinical episodes are treated with formal-sector care. We also assume that 100% of severe malaria episodes are treated.

Effective treatment.

We assume that 100% of clinical episodes are treated with formal-sector care and that there are no treatment failures. Moreover, we assume that all severe episodes receive in-patient treatment.

Anti-pyretic treatment.

We assume the same anti-malarial treatment coverage as in the reference scenario, but in addition we assume that 50% of episodes are treated at home by paracetamol. The paracetamol is assumed to provide only symptomatic relief and thus to have no effect on the epidemiologic outcomes.

This defined the baseline status of the simulated populations. We ran simulations over a 90-year period at different transmission intensities under the assumptions of the reference case management scenario. The rather low level of treatment in this scenario is intended to approximate conditions prevailing in many areas studied in Africa of limited drug availability, drug resistance, and non-treatment or under-treatment of minor febrile attacks.

To explore the dynamic impact of different case management options, we then simulated the transient behavior over the next 5-, 10-, and 20-year periods for different case management scenarios, assuming the vectorial capacity for P. falciparum transmission to follow the same seasonal pattern as during the baseline period. We compared outcomes with those of scenarios in which the reference case management regimen continued.

Costing.

Both marginal and average costs of health care were computed. The marginal cost of treatment is the additional financial or opportunity costs that is incurred when treating each additional case, but does not include the fixed cost of the infrastructure. The average costs include all those costs involved in delivering the intervention, including the use of spare capacity, and those health care resources diverted from other uses.30

Uncomplicated malaria.

Direct costs of an uncomplicated malaria case seeking care at formal-sector facilities, Cdo, comprise the cost of an out-patient visit, the cost of drug treatment, and other costs incurred by the patients, i.e.,

Cdo=Do+Vo+Ho

where Ho is the patient (household) cost when visiting formal-sector outpatient facilities (excluding fees), Do is the cost of out-patient drug treatment, and Vo is the non-drug costs of an out-patient visit. Do is computed as

Do=DodLd(1+W)

where Dod is the cost of drug per day and Ld is the number of days of therapy. The drug regimens and thus price depend on patient age and weight (Table 4), with the prices, which include distribution costs to districts, corresponding to those in the medical store department catalog31 of the Tanzanian Ministry of Health. W, the % additional cost of drug wastage, takes a value of 25% throughout.32

The non-drug cost of an outpatient visit is computed from published data on proportions of out-patients reporting at different levels of the health system, on the proportion, pt, of cases undergoing diagnostic tests, and on unit costs after exclusion of drug costs (Table 6). In the average analysis, the non-drug cost, Vao, is thus given by

Vao=phcVhc+phVh+pdVd+ptT.

In the case of marginal costs there is an adjustment for the proportion of recurrent non-fixed costs, i.e.,

Vmo=Vaopro(1prfo).

The patient (household) costs per outpatient visit, Ho, comprise travel expenses, expenses related to medical supplies Hm, and non-medical supplies, Hn, such as the purchases of food and drinks or costs of spending the night away from home while seeking care33 (Table 6) so that

Ho=Ht+Hm+Hn

In self-treatment it is assumed that patients do not incur in any additional costs to purchase the drug because drugs are likely to be purchased from a private shop close to the patient’s home.

Severe malaria.

The direct health care costs of a severe malaria case Cdi are given by

Cdi=Di+Vi+Hi

where Vi is the non-drug cost of in-patient care, Di is the cost of drug treatment, and Hi is the patient (household) cost when visiting formal-sector in-patient facilities. Di is computed by multiplying the costs by the duration for which they are incurred. During the first day of treatment, the drug dosage and consequently the costs are different, so overall Di is given by

Di=(Di1+Di2(Li1))(1+W)

where Di1 is the cost for the first day, Di2 is the cost per day thereafter, and Lt is the length of treatment (in days) (Table 6). The non-drug cost of in-patient care in the average analysis is given by

Vi=Vai=NiLi(o)

where Li(o) is the average length of stay, which varies depending on the outcome o, and Ni is the in-patient cost (Table 6). Correspondingly, in the marginal analysis the non drug cost is

Vi=Vmi=NiLi(o)pri(1pfi).

The costs incurred by patients are the same as for an outpa-tient visit for the first day. For subsequent days of stay, we include only the costs of medical and non-medical supplies (Hm and Hn respectively) so that

Hi=Ht+(Hm+Hn)Li(o).

RESULTS

Reference scenario simulation.

Simulated patterns of age-prevalence and age-incidence for the reference scenario (Figure 2) are similar to those for typical meso-endemic settings in Africa to which the models were fitted.9,12,13 The direct cost per capita is stable over time. The predicted infectiousness of the host population, κ̄u(t), fluctuates seasonally around a value of approximately 3% (Figure 3a). Since the reference scenario uses the same transmission pattern and health system to construct the baseline population as are applied during the follow-up, there is no trend over the 20-year simulation period in these epidemiologic variables or in the treatment costs.

Over the 20-year simulation period, the total number of undiscounted DALYs lost due to malaria in our population of 100,000 people is approximately 481,000, which corresponds to a rate of 0.24 DALYs per capita per year. Since most of these DALYs are due to mortality, the total number of YLLs is very close to that of DALYs (Table 7). If YLLs and DALYs are discounted at a standard rate of 3%, the total number of DALYs is considerably lower.

The total undiscounted direct average costs to treat malaria episodes with the reference case management model amounts to US$ 485,793 over the 20-year simulation period. This corresponds to US$ 4.86 per capita and, on average, US$ 0.24 per capita per year (Table 7). Out-patient visits account for 32% of total direct costs, drug treatments of both uncomplicated and severe episodes for 7%, hospital admissions of severe episodes for 40%, and patient costs for 22%. The marginal cost, i.e., additional financial or opportunity costs that would be incurred when introducing a new control intervention, is approximately 58% of the average cost.

Effect of changing levels of access to case management.

Comparison of the reference scenario with the extreme scenario with no treatment of malaria episodes (either uncomplicated or severe) showed noticeable epidemiologic effects of treatment despite the low attendance rates for uncomplicated episodes in the reference health system. In children less than 10 years of age, the no treatment scenario predicted higher prevalence of infection (Figure 4), a higher anemia prevalence (Figure 5), and a slight increase in the incidence of clinical episodes, with age patterns as shown in Figure 6a–c. There was only a small effect on the incidence of severe malaria (Figure 6d–f). Since the reference health system includes a relatively high treatment rate of severe episodes, the largest differences between the no treatment and reference scenarios were in the mortality rates, with a substantially higher mortality rate predicted with no treatment, especially in the second half of the first year of life (Figure 6g–i).

The reference scenario is in a state of equilibrium throughout the simulation, although there is stochastic variation over time in the outputs. The no treatment scenario quickly reaches a new equilibrium. Therefore, only the average prevalence over 20 years is shown for this scenario (Figure 4), and the effects on incidence of morbidity and mortality do not change much during the follow-up period (Figure 6). The total number of DALYs lost over the simulated 20-year period was 13% higher with the no treatment regimen than with the reference. The effect on transmission, as measured by κ̄u(t) is negligible.

The complete coverage scenario for treatment leads to a rapid decrease in transmission, as measured by κ̄u(t) (Figure 3b). This stabilizes quickly at a value approximately 60% of that in the reference scenario, implying that treatment of all the clinical episodes (including minor episodes) can reduce the inoculation rate by about 40%. Complete coverage predicted very substantial decreases in prevalence of parasitemia (Figure 4), anemia (Figure 5), and incidence of uncomplicated episodes (Figure 6), but these outcomes, which reflect the dynamics of immunity, required an extended period to reach equilibrium. Although treatment of severe episodes in the complete coverage health system is no different from the reference, the effects on transmission and persistence of parasites result in substantial reductions in incidence of severe morbidity and mortality (Figure 6), leading to a total number of DALYs lost over 20 years of only approximately 45% of those in the reference scenario (Table 7).

The epidemiologic effects of high treatment coverage were concentrated in the youngest age groups, resulting in a substantial shift in the age of peak incidence of uncomplicated episodes (to older ages) and of mortality (to younger ages, in which a greater proportion of the mortality is contributed by indirect deaths). Since the changes in the age-prevalence and age-incidence curves caused by complete coverage were also time-dependent, transient effects can be seen throughout the 20-year follow-up period. As a result of the shifts in age-incidence, 10 years into the simulation an increase in incidence of clinical episodes above baseline levels is evident in individuals more than 10 years of age (Figure 6b). Since the shifts in the peak of the incidence curves to older age-groups accumulates over time, the benefit of the intensive treatment regimen decreases with time.

The distribution of direct costs is also changed as a function of treating all malaria episodes with a first-line drug. In the scenarios that we simulated, there would then be little need for second-line treatment; thus, many severe episodes could be prevented, which in turn reduces in-patient costs. Our model predicts that if all uncomplicated episodes were treated with the first-line drug, out-patient visit costs would account for 61% of total direct costs, drug treatments for 7%, inpatients admissions for 3%, and patient costs for 30%. The total direct costs to treat all malaria episodes would be approximately 7.4-times those of the reference scenario.

The moderate coverage scenario predicts effects on prevalence and on the clinical outcomes (Figures 4–6) more similar to those for complete coverage than to those for no treatment. This is despite the assumption in the moderate coverage health system of treatment rates for uncomplicated episodes much less than 50% and thus much closer to those for no treatment than those for complete coverage. This implies that within our models, there is a highly non-linear relationship between health outcomes and treatment coverage for uncomplicated malaria, with a very high marginal impact of increases in coverage when it starts from a low level. This conclusion is supported by the simulation of effective treatment, which gave very similar results to that of complete coverage for all the outcomes except mortality. Mortality rates and thus DALYs lost (Table 7) were reduced by the effective treatment health system to substantially below those with the complete coverage health system because all severe cases were assumed to be treated as in-patients.

The Abuja target coverage simulation is intended to simulate the impact of achievement of the coverage of 60% targeted in the Abuja Declaration on Roll Back Malaria in Africa, signed by African Heads of State and Government in April 2000. The YLLs, DALYs, and costs are intermediate between those predicted for the reference and those for full coverage.

The antipyretic treatment simulation is intended to indicate the sensitivity of the costs to allowance for the large number of people who self-treat with anti-pyretics, in addition to those who use anti-malarials. Unfortunately, it is difficult to obtain good estimates for actual levels of self-treatment in sub-Saharan Africa. The coverage of 50% for self-treating with anti-pyretics that we use is associated with an increase in drug costs of between 9% and 16% (Table 7), which indicates that although this is not likely to be a factor dominating costs, it could be of some importance because these are out-of-pocket expenses paid predominantly by poor patients. It would be important to include better estimates of drug choice and coverage for self-treatment.

Effect of transmission intensity.

In higher transmission settings, simulated parasite prevalence was higher, and peaked at a younger age (Figure 2a). The incidence of uncomplicated malaria episodes also increased with transmission intensity in young children, but the reverse pattern was observed in older individuals (Figure 2b), matching the pattern to which the model was fitted.13 The incidence of severe episodes showed a similar pattern, but with a steeper decrease in incidence with age at high transmission, and consequently a crossing of the age-incidence curves at younger age (Figure 2c). The pattern for mortality was similar, with the mortality rate independent of transmission intensity at the age of approximately 3–4 years.

The average level of transmission to the vector, κ̄u(t), was similar to that for the reference scenario for all values of EIR investigated, but the amplitude of the seasonal variation in κ̄u(t) increased with the transmission intensity.

The total number of YLLs and DALYs lost over the simulated 20-year period are only slightly higher in the high transmission settings compared with areas of lower transmission intensity. The total direct costs are determined by the number of uncomplicated and severe episodes treated, which are higher than in the reference scenario in the low transmission setting and lower in the high transmission setting (Figure 7). However, these figures depend strongly on the model predictions for rates of severe malaria in adults, of which we are highly uncertain.12

Changing access to case management in different malaria transmission intensity settings.

The effects of an increased or decreased level of access to case management also vary according to the prevailing malaria transmission intensity (Figure 8). In a setting of moderate malaria transmission, treating all uncomplicated episodes over 20 years would lead to only a small difference in the total number of uncomplicated episodes, but reduces incidence of severe episodes by 49%, and the number of deaths and DALYs lost by 57% (Table 7).

In the low transmission setting, treating all uncomplicated cases over 20 years reduces incidence of uncomplicated episodes by 71%, severe episodes by 88%, and the number of deaths and DALYs lost by 83%. In the high transmission setting, complete treatment coverage would increase the total number of uncomplicated episodes over time, and would lead to a reduction of only 31% of severe episodes and DALYs lost and 34% of the number of deaths.

Treating everyone has a much greater effect on incidence at low transmission intensities. At high transmission, a high level of coverage always appears to be beneficial in terms of reducing incidence of severe episodes and of mortality, but may even lead to an increase in incidence of uncomplicated episodes. Within the model, this is because a very high treatment rate is associated with a reduction in exposure to asexual blood stage parasites and thus in acquired blood-stage immunity.

The economic implications of changing levels of access to case management also differ according to the malaria transmission intensity. Simulation over a 20-year period under the assumption of complete treatment coverage of uncomplicated malaria episodes would increase direct costs by a factor of almost 10 in a highly endemic setting, but the increase would be only 92% in low transmission settings (Table 7).

DISCUSSION

We present a first attempt to use a dynamic model for case-management of malaria in sub-Saharan Africa. For prediction of the effects of the case management, we considered a range of different transmission intensities characteristic for large parts of malaria-endemic Africa, and our simulations are thus likely to be of broad applicability. Lower EIRs than considered here (i.e., less than five infectious bites per person per year) are characteristic of highly urbanized settings, the African highlands, and areas located at the current distribution edges of P. falciparum transmission.34,35 Our model needs further development and validation to make meaningful predictions for such settings.

Our modeling approach expands the scope for predictions of the epidemiologic and economic consequences of malaria interventions as a direct function of the case management. In a first step, we have simulated different rates of treatment coverage, including the most extreme scenarios of either complete lack of treatment or full coverage. These two scenarios, together with a reference scenario largely constructed from real data obtained from Tanzania, were used for simulations up to 20 years. Costs were also built into our dynamic models, which will ultimately make it possible to predict the cost-effectiveness of the case management.

Our immediate purpose is to integrate effects of case management into our dynamic models of the clinical epidemiology and natural history of P. falciparum malaria in a typical setting of sub-Saharan Africa. This approach could readily be adapted to assess the costs of scaling up malaria treatment but this would entail more detailed analysis of the activities involved in changing treatment practices.

Our model can be used to make predictions of the effect of introducing a new malaria control intervention (e.g., malaria vaccine) or scaling-up of existing control measures (e.g., ITNs). The former motivated the development of our modeling approach. The current model is probably better at fulfilling this objective than in capturing the impact of changes in case management, including different levels of treatment and changes in national antimalarial drug policies. This is justified because the epidemiologic model was fitted mainly to cross-sectional data from various settings across sub-Saharan Africa. Since it is less able to capture longitudinal patterns within hosts, it does not claim to incorporate realistic patterns of treatment-seeking behavior or of referral patterns. In African settings where patients have limited resources, care-seeking patterns in general and malaria treatment-seeking behavior in particular are complex.3638

There is a need to build on simple models of the referral system32 so that we become more confident of the likely impacts of changes in national antimalarial drug policies. For example, parasite resistance to SP has reached critical levels in many parts of central and east Africa, including Tanzania,39,40 and this places a question mark against our longer-term predictions of cost-effectiveness, which assume that treatment with SP remains efficacious. In view of the public health, social, and economic significance of SP resistance, efforts are underway in Tanzania and elsewhere to change national policies towards artemisinin-based combination therapy (ACT). The Global Fund to Fight AIDS, Tuberculosis, and Malaria has recently approved a project to switch from SP (and amodiaquine) to ACT.41 Such a shift in drug policy is of considerable public health significance and will directly affect the case management of P. falciparum malaria. There is a need to adapt our model to field data from a range of different settings, and that will make it possible to explore the epidemiologic and economic consequences of the case management system under different scenarios. These should include simulation of the shift from SP to ACT conditional on various levels of SP resistance. All of these simulations need to take into account patterns of self-treatment, for which we currently have only weak data.

Regarding the epidemiologic model, we chose to define the seasonal pattern of P. falciparum transmission by using data from the village of Namawala in Tanzania. The high level of transmission measured there, even in comparison to other sites in Tanzania,22,42 made it possible to measure the intensity of transmission during the dry season. Multiplication of the Namawala rate by a constant therefore provides us with a reasonable estimate of the seasonal pattern, even for lower transmission areas where dry season transmission usually cannot not be measured.

The national malaria control program of Tanzania reports that 75% of people live in areas of stable malaria transmission, 17% in areas of unstable transmission (duration of transmission less than one month per year), and the remaining 8% in areas of unstable transmission (highly seasonal).29 However, historic and contemporary maps of malaria endemicity for Tanzania43,44 do not provide estimates of the inoculation rate with which to determine the distribution of EIR levels among the people within areas of stable transmission.

Our approach makes it possible to look at how such variations in transmission intensity might affect the impact of changes in the health system. However, our confidence in the present results is limited by uncertainties in our epidemiologic models (especially that for severe malaria and mortality, for which we had no data for older age groups12).

Increasing levels of treatment generally shift the age-prevalence and age-incidence curves so that the peaks are in older age-groups. We developed our parasitologic model mainly using archive data that predated the widespread use of anti-malarial chemotherapy. A delayed peak in the age-prevalence curve that we attribute to this effect was already apparent in the dataset from Navrongo, Ghana45 which was from a more recent period than the other studies.9 The effect of treatment on reducing acquired blood-stage immunity is very uncertain because asexual blood stage immunity is modeled as a function of both the number of distinct infections and of the cumulative parasite load, and we do not know what should be the relative contributions of these two different components of acquired immunity. The effects of cumulative parasite load are intended to simulate acquisition of immunity to antigenic variants that arise during the course of the infection.

We agree with other models for cost-effectiveness of malaria interventions in attributing most of the burden of disease to mortality rather than to disability associated with acute illness, sequelae, or anemia. Important methodologic issues requiring further investigation arise in the computation of the DALYs. In African populations with high infant mortality, there is generally an increase in life expectancy during the first few years of life, and this leads to perverse outcomes in the computation of DALYs if the effect of an intervention is partly to shift mortality to older ages in childhood. For example, if life expectancy at one year of age is 64 years, and life expectancy at five years of age is 72 years, then the number of life years gained by shifting age at death would be negative: 64–72 = −8. This effect is accentuated by discounting or age-weighting of the DALYs, but does not arise with the Japanese life tables used to compute DALYs in the GBD calculations used by the World Health Organization.17 We did not use these life tables because it is generally considered that local life tables should be used to compute DALYs in cost-effectiveness analyses,46 but there is a strong case for using death rates that exclude the health effect under investigation. For the present analyses, we used a life table from an east African site with low malaria incidence. In these life tables, where malaria plays only a small role, there is an increase in life expectancy over the first few years of life.

In conclusion, we have made a first attempt to develop a modeling framework to simulate the dynamic effects of the case management of P. falciparum malaria across a wide range of transmission intensities in sub-Saharan Africa. We discovered several deficiencies in our understanding of the relevant health systems. Our simulations of a range of scenarios indicate which of these uncertainties are most likely to be important for the prediction of cost-effectiveness of malaria interventions. Further development of our modeling approach offers more realistic evaluation of the epidemiologic and economic consequences of malaria interventions. This in turn will create a sound foundation for measuring the effects of introducing new antimalarial interventions (e.g., malaria vaccines), or scaling up those that are already known to be efficacious and cost-effective.

Table 1

Model inputs used for efficacy and malaria treatment-seeking behavior*

Case management scenarios
Symbol Description No treatment Reference Moderate coverage Complete coverage Effective treatment Reference
* The values for the reference scenario are adapted from those used in our simulation of a field trial of a malaria vaccine; those for the moderate coverage scenario are based on the data of the Tanzanian National Malaria Control Program.29 SP = sulfadoxine-pyrimethamine; NA = not applicable.
† The cure rate refers to the “adequate clinical response rate.”
‡ The same probabilities are used for neurologic sequelae for both in-patients and non-hospitalized severe episodes.
Uncomplicated malaria
P u     Probability of seeking care in the formal health sector 0.0 0.04 0.27 1.0 1.0
P s     Probability of self-treatment 0.0 0.01 0.13 0.0 0.0
P r     Probability of seeking out-patient care in case of treatment failure 0.0 0.04 0.27 1.0 1.0
Compliance
C u     SP: formal health sector NA 0.90 0.90 0.90 1.00 32
C r     Amodiaquine NA 0.45 0.45 0.45 1.00 32
C s     SP: self-treatment NA 0.85 0.85 NA NA 32
Cure rate†
R u     SP: formal health sector NA 0.93 0.93 0.93 1.00 32
R r     Amodiaquine NA 0.85 0.85 0.85 1.00 32
R s     SP: self-treatment NA 0.63 0.63 NA NA 32
% of non-compliers for whom treatment is effective
R ns     SP NA 0 0 NA NA
R ns     Amodiaquine NA 0.20 0.20 NA NA 32
Severe malaria
P h     Probability of in-patient care 0.0 0.48 0.48 1.0 1.0 26
R q     Cure rate (quinine) NA 0.998 0.998 0.998 0.998 31
R x     Probability of neurologic sequelae for severe episodes for age-group
        < 5 years of age‡ 0.0132 0.0132 0.0132 0.0132 0.0132 32,47
    Probability of neurologic sequelae for severe episodes for age-group
        ≥ 5 years of age‡ 0.005 0.005 0.005 0.005 0.005 32,47
Table 2

Disability weights and duration of disability used to calculate YLDs*

Disease condition Disability weight Duration (years)
* YLDs = years of life with disability; ND = not defined.
Untreated neurologic sequelae 0.473 35.4
Neurologic sequelae (treated) 0.436 35.4
Uncomplicated malaria episode 0.211 0.01
Anemia 0.012 ND
Low birth weight ND ND
Others ND ND
Table 3

Scenarios modeled: health systems and transmission intensities*

Scenario Annual EIR
* EIR = entomologic inoculation rate. EIR changes over time in these scenarios.
Transmission intensities
    Very low 1.3
    Low 5.2
    Reference 21
    High 83
    Very high 329
Health system
    No treatment
    Reference
    Moderate coverage
    60% Abuja target coverage
    Full coverage
    Effective treatment
    Antipyretic treatment
Table 4

Sulfadoxine-pyrimethamine and amodiaquine doses and costs, by age and weight*

Regimen, age and weight categories No. of tablets Cost per course in U.S.$1,000 Cost per course in U.S.$2004
* Sulfadoxine-pyrimethanine is administered as a single dose. Amodiaquine values are the number of 200-mg tablets in a three-day course.31
Sulfadoxine-pyrimethamine
    < 1 year (< 11 kg) 0.5 12.4 0.012
    1–5 years (11–19 kg) 1 24.8 0.024
    6–9 years (20–30 kg) 1.5 37.2 0.035
    10–14 years (31–45 kg) 2 49.6 0.047
    ≥ 15 years (> 45 kg) 3 74.4 0.071
Amodiaquine
    < 1 year (< 11 kg) 1.25 18.75 0.018
    1–3 years (11–15 kg) 1.75 26.25 0.025
    4–5 years (16–19 kg) 2.25 33.75 0.032
    6–8 years (20–25 kg) 3 45 0.043
    9–11 years (26–36 kg) 4.25 63.75 0.061
    12–14 years (37–50 kg) 6.25 93.75 0.089
    15–16 years (51–60 kg) 7.5 112.5 0.107
    ≥ 17 years (> 60 kg) 8 120 0.114
Table 5

Intravenous quinine doses and costs, by age and weight

Age and weight categories Dose Cost per day in Tz shillings Cost per day in U.S.$2004 Cost per course in U.S.$2004
Initial dose (20 mg/kg over 4 hours)
    < 1 year (< 11 kg) 180 54 0.051
    1–3 years (11–15 kg) 240 72 0.069
    4–5 years (16–19 kg) 360 108 0.103
    6–8 years (20–25 kg) 420 126 0.120
    9–11 years (26–36 kg) 600 180 0.171
    12–14 years (37–50 kg) 840 252 0.240
    15–16 years (51–60 kg) 1,080 324 0.309
    ≥ 17 years (> 60 kg) 1,200 360 0.343
Dose per day thereafter (10 mg/kg every 8 hours for 6 days)
    < 1 year (< 11 kg) 280 81 0.077 0.514
    1–3 years (11–15 kg) 360 108 0.103 0.686
    4–5 years (16–19 kg) 540 162 0.154 1.029
    6–8 years (20–25 kg) 630 189 0.180 1.200
    9–11 years (26–36 kg) 900 270 0.257 1.714
    12–14 years (37–50 kg) 1,260 378 0.360 2.400
    15–16 years (51–60 kg) 1,620 486 0.463 3.086
    ≥ 17 years (> 60 kg) 1,800 540 0.514 3.429
Table 6

Health-seeking behavior and unit cost assumptions

Item Description Value Reference
* Daily average household (patient) out of pocket costs.
Household (patient costs)*
H t     Travel cost (US$) 0.08 33
H m     Medical supplies (US$) 0.03 33
H n     Non-medical supplies (US$) 0.19 33
Uncomplicated malaria
p hc     % of out-patient visits that take place at health centers 18% 41
p d     % of out-patient visits that take place at dispensaries 72% 41
p h     % of out-patient visits that take place at hospitals 10% 41
V hc     Cost per out-patient visits at health centers (US$) 1.27 33
V d     Cost per out-patient visits at dispensaries (US$) 1.02 33
V h     Cost per out-patient visits at hospitals (US$) 2.10 48
p t     % diagnostic tests (proportion of patients) 10% 29
T     Unit cost of diagnostic tests (proportion of patients) 0.30 29
p ro     % of out-patient visit cost that are recurrent 69% 29
p rfo     % of out-patient visit recurrent cost that are fixed 25% 32
H o     Average patient cost (US$) 0.30 33
Severe malaria
N i     Non-drug cost per day of stay - (US%)
        (Capital) 2.30 49
        (Recurrent) 5.50 49
        (Total) 7.80 49
Li(1)     Average length of stay when patient fully recovers 4.50 32
Li(2)     Average length of stay when patient recovers with neurologic sequelae 10 32
Li(3)     Average length of stay when patient dies 2 32
p ri     % of in-patient costs that are recurrent 71% 47
p fi     % of in-patient recurrent cost that is fixed 50% 32
Table 7

Years of life lived with disabilities (YLLs),* disability adjusted life-years,* and direct costs†

Undiscounted Discounted (3%)
YLLs DALYs Average costs Marginal costs YLLs DALYs Average costs Marginal costs
* Lost per capita per year due to malaria.
† Direct cost per capita in US$ per year.
‡ Same transmission level as in reference scenario.
§ Epidemiologic outcomes as per reference scenario.
Reference 0.238 0.244 0.243 0.142 0.120 0.125 0.184 0.108
Moderate coverage‡ 0.217 0.224 1.066 0.736 0.112 0.118 0.809 0.558
60% Abuja target coverage‡ 0.160 0.165 1.423 0.946 0.083 0.087 1.053 0.70
Full coverage‡ 0.100 0.105 1.807 1.212 0.052 0.056 1.463 0.993
Effective treatment‡ 0.081 0.086 1.424 0.918 0.042 0.046 1.054 0.679
No treatment‡ 0.276 0.276 0.138 0.143
Antipyretic treatmentठ0.238 0.244 0.266 0.165 0.120 0.125 0.201 0.125
Very low transmission 0.219 0.226 0.285 0.172 0.119 0.125 0.216 0.131
Low transmission 0.224 0.231 0.283 0.169 0.118 0.124 0.215 0.129
High transmission 0.242 0.246 0.204 0.116 0.120 0.123 0.155 0.088
Very high transmission 0.234 0.237 0.169 0.095 0.115 0.117 0.128 0.072
Low transmission, full coverage 0.036 0.038 0.544 0.368 0.017 0.018 0.470 0.321
High transmission, full coverage 0.160 0.165 2.027 1.349 0.068 0.072 1.643 1.109
Figure 1.
Figure 1.

Decision tree pathways. na = not applicable.

Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 75, 2_suppl; 10.4269/ajtmh.2006.75.90

Figure 2.
Figure 2.

Predicted age-prevalence and age-incidence curves by transmission intensities The reference scenario is the transmission intensity observed at Namawala, Tanzania divided by a factor 16. Low transmission = Namawala transmission divided by 64; high transmission = one-fourth of Namawala transmission; very high transmission = transmission observed at Namawala. a, age-prevalence curve of patent parasit-emia; b, age-incidence curve of uncomplicated episodes; c, age-incidence curve of severe episodes; d, age-incidence curve of mortality.

Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 75, 2_suppl; 10.4269/ajtmh.2006.75.90

Figure 3.
Figure 3.

Infectivity of the human population. a, reference scenario; b, scenario assuming full treatment coverage.

Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 75, 2_suppl; 10.4269/ajtmh.2006.75.90

Figure 4.
Figure 4.

Age-prevalence curves of parasitemia under different case management scenarios during a simulated 20-year follow-up period. ▪ = no treatment; ▵ = reference; ▴ = moderate coverage (first year of follow-up); * = complete coverage (first year of follow-up); ○ = complete coverage (10th year of follow-up); • = complete coverage (20th year of follow-up).

Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 75, 2_suppl; 10.4269/ajtmh.2006.75.90

Figure 5.
Figure 5.

Age-prevalence curves of anemia (hemoglobin level < 8 g/dL) The reference scenario is the transmission intensity observed at Namawala, Tanzania divided by 16. Low transmission = Namawala transmission divided by 64; high transmission = one-fourth of Namawala transmission; very high transmission = transmission observed at Namawala.

Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 75, 2_suppl; 10.4269/ajtmh.2006.75.90

Figure 6.
Figure 6.

Age-incidence curves under different case management scenarios at different durations of simulation during a 20-year follow-up period. a–c, age-incidence of uncomplicated episodes; d–f, age-incidence of severe episodes; g–i, age-incidence of mortality.

Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 75, 2_suppl; 10.4269/ajtmh.2006.75.90

Figure 7.
Figure 7.

Direct costs in relation to transmission intensity. Upper line = undiscounted; lower line = discounted.

Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 75, 2_suppl; 10.4269/ajtmh.2006.75.90

Figure 8.
Figure 8.

Effect of changing case management in different transmission settings. The status of the population at baseline was defined by simulating the reference health system for 90 years for each transmission intensity. The follow-up period then ran for 20 years with the chosen health system, and the results are the average for the 20 years. The incidence rates quickly settled to a new level. Because of the uncertainty in the rates of severe morbidity and mortality in adults, the predictions for only for children less than 10 years of age are shown. ▪ = no treatment; ▵ = reference case management; × = full coverage.

Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 75, 2_suppl; 10.4269/ajtmh.2006.75.90

*

Address correspondence to Thomas Smith, Swiss Tropical Institute, PO Box, CH-4002 Basel, Switzerland. E-mail: Thomas-A.Smith@unibas.ch

Authors’ address: Fabrizio Tediosi, Nicolas Maire, Thomas Smith, Guy Hutton, Jürg Utzinger, Amanda Ross, and Marcel Tanner, Swiss Tropical Institute, PO Box, CH-4002 Basel, Switzerland, Telephone: 41-61-284-8273, Fax: 41-61-284-8105, E-mails: fabrizio.tediosi@unibas.ch, nicolas.maire@unibas.ch, Thomas-A.Smith@unibas.ch, guy.hutton@unibas.ch, juerg.utzinger@unibas.ch, amanda.ross@unibas.ch, and marcel.tanner@unibas.ch.

Acknowledgments: We thank Dan Anderegg for editorial assistance, and members of the Technical Advisory Group (Michael Alpers, Paul Coleman, David Evans, Brian Greenwood, Carol Levin, Kevin Marsh, F. Ellis McKenzie, Mark Miller, and Brian Sharp), the Project Management Team at the Program for Appropriate Technology in Health (PATH) Malaria Vaccine Initiative, and GlaxoSmithKline Biologicals S.A for assistance in this study.

Financial support: The mathematical modeling study was supported by the PATH Malaria Vaccine Initiative and GlaxoSmithKline Biologicals S.A.

Disclaimer: This publication and the contents hereof do not necessarily reflect the endorsement, opinion, or view points of the PATH Malaria Vaccine Initiative or of GlaxoSmithKline Biologicals S.A.

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Author Notes

Reprint requests: Thomas Smith, Swiss Tropical Institute, Postfach, CH-4002 Basel, Switzerland.
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