INTRODUCTION
As part of the enlarged global efforts to control malaria, production of candidate malaria vaccines at clinical grade has significantly increased.1 Vaccines designed to be effective against specific stages of parasite development have different endpoints of efficacy in various target groups. Pre-erythrocytic vaccines may primarily be used for travelers from non-endemic areas to prevent blood stage infection. Asexual blood stage vaccines will primarily be targeted at young children in endemic areas to control parasitemia, resulting in reduction of morbidity and mortality. A long-term goal may be a multi-antigen, multi-stage vaccine that inhibits pre-erythrocytic stages, asexual parasite growth, and mosquito stage development.
Evaluation of vaccine candidates in clinical trials is a cornerstone in the selection process of product development. Downstream, selection of vaccine candidates is based on safety and immunogenicity profiles (Phase I). Vaccine efficacy can be tested by experimental infections in humans (Phase IIa) or by naturally acquired infections in malaria-endemic areas at a small (Phase IIb) or larger scale (Phase III). Experimental infections for testing pre-eythrocytic vaccines in humans have used laboratory-reared Plasmodium falciparum–infected mosquitoes.2–4 Study endpoint with curative chloroquine treatment, is usually determined by first occurrence of parasitemia as detected by microscopy. Mild clinical symptoms of malaria are often seen in volunteers during phase IIa trials.5 This approach has seemed inappropriate for the evaluation of asexual stage vaccines because of potential safety risks and discomfort associated with the lengthy exposure to symptomatic malaria necessary to measure vaccine efficacy. Recently, a sensitive quantitative real-time polymerase chain reaction (PCR)6 has been developed for P. falciparum parasites.
In this study, human experimental P. falciparum malaria infections initiated by mosquito bites were combined with quantitative real-time PCR measurement of parasites in the blood. We observed a remarkably limited variation in parasitemia profiles within and between non-immune volunteers, allowing the development of a statistical model. The model was used to provide estimates of parameters of parasite life cycles and multiplication rates, and could be used to predict the result of pre-erythrocytic and asexual stage vaccines with different degrees of efficacy. Application of this model will significantly improve the capacity to evaluate both malaria vaccines in clinical phase IIa trials.
MATERIALS AND METHODS
Experimental malaria infection of human volunteers.
Anopheles stephensi mosquitoes were maintained in the insectary at the animal house (University Medical Center, Nijmegen, The Netherlands). Three-day-old mosquitoes were fed on blood containing gametocytes7 produced in a standardized semi-automated culture system seeded with the chloroquine-sensitive NF54 isolate of P. falciparum.8 Mosquitoes were allowed to blood feed for 10 minutes and fed and unfed mosquitoes were separated three hours later. Oocysts and sporozoite counts were performed 7 and 14 days after the feed, respectively, and batches with more than 90% infected mosquitoes were used for experimental infection of volunteers. Healthy volunteer (mean age = 28.3 years, range = 18–39) with no prior exposure to malaria were recruited after informed consent was obtained. Sets of seven female mosquitoes that were deprived of sugar for 17 hours were exposed to bites on both forearms for 10 minutes. This procedure was repeated until at least five mosquitoes that contained salivary glands sporozoites upon subsequent dissection had fully engorged. Three experiments with each five volunteers were conducted. All 15 volunteers were followed by daily blood films and for malaria symptoms from day 4 onwards. In experiments 1 and 3, volunteers were immediately treated with a standard dose of chloroquine upon microscopic detection of parasites. In experiment 2, treatment was extended for 48 hours after the thick blood smear became positive. During this period, symptomatic treatment was provided. Clinical condition assessed by a study-independent physician. Parasites were counted against 500 white blood cells in Giemsa-stained thick smears. The quantitative real-time PCR to determine the densities of P. falciparum parasites has been described in detail.6 Briefly, P. falciparum standard curves were prepared by DNA extraction from titrated samples of purified NF54 ring-infected cells and measured by the quantitative real-time PCR. The standard curve is defined as the correlation between the quantitative real-time PCR threshold cycles and amounts of titrated ring-stage parasites measured as DNA. The number of parasites in the sample was calculated from the threshold cycles using linear regression. These studies were reviewed and approved by the Ethical Committee of the University Medical Center Nijmegen (CWOM 0004-0090, 0011-0262, and 2001/203, respectively).
Statistical analysis.
Observed parasite densities per milliliter of blood were described by a non-linear model as a function of days since infection, mimicking successive cycles of appearance and disappearance (sequestration) of ring form generations (Figure 1). Table 1 gives a glossary of the nine parameters in the model.
The longitudinal nature of the data makes individual observations serially dependent on each other. In particular, if the initial number of ring forms for an individual is high (due to many infected liver cells), all measurements in subsequent cycles are expected to be high. Also, if the first appearance of ring forms is late (e.g., due to delay in establishment of the infection) all further events are delayed, as is clearly visible for the timing of events for one individual in Figure 2c (purple). We therefore estimated the number of infected hepatocytes X and mean duration until first appearance of ring forms μ1 for each individual separately. Given the values of X and μ1, we assumed mutually independent measurement error to be the source of differences between model predictions and observations. Parameters μ2, μ3, σ12, σ22, σ32, β1, and β2 were considered biologic constants and assumed equal for all individuals and constant over time; the number of observations per individual volunteer did not allow more detailed estimates of these parameters. The product of the number of infected hepatocytes X and the number of ring forms per infected hepatocyte per milliliter of blood β1 is fully determined by the maximum number of ring forms in the first cycle, and both parameters cannot be estimated separately. The value of β1 was therefore set at 6.0 ring forms per hepatocyte per milliliter, based on 30,000 merozoites9,10 per hepatocyte and an average of 5 liters of blood per person.
Values of parameters were estimated by fitting the model to the observations using log least squares, i.e., assuming measurement error of log transformed values to be normally distributed. A quantity of 10 parasites/ml, i.e., half the detection limit of the PCR method, was added to the values before taking logarithms to avoid giving too much weight to values near zero. Different models were compared by the likelihood ratio test with differences in −2 log likelihood between two models following a chi-square distribution. It appeared that a model with the same variance for duration of ring forms σ22 and sequestration σ32 was not significantly worse compared with a model using both parameters separately (P = 0.45). We therefore let σ22 = σ32. Similarly, a model with different values of μ1 for each individual was highly superior to a model with one value (P = 0.01), supporting the choice of considering μ1 an individual parameter. Confidence intervals were determined by re-fitting the model for a range of pre-set values of each parameter, and assessing both values where −2 log likelihood differed by 3.84 (i.e., χ2 with one degree of freedom) with the best fitting model.
The model was programmed in Microsoft (Redmond, WA) Excel® 2000 and the Solver option was used for maximizing the likelihood. The resulting model fitted the data very well. Residual plots of log (+10) transformed values showed a consistent (small) error with time for each individual, suggesting no important serial dependency between individual observations (not shown). The effect of a pre-erythrocytic vaccine was simulated by a reduction of the initial number of infected hepatocytes X. The effect of an asexual stage vaccine was simulated by a reduction of the number of ring forms per hepatocyte per milliliter of blood β1 and the multiplication factor β2.
RESULTS
A total of 15 volunteers (groups of five subjects in three experiments) were experimentally infected by bites of 4–7 mosquitoes. Onset of blood infection was assessed microscopically by thick smear twice a day from day 4 post-infection until treatment. All volunteers developed parasitemia (mean = 8.7 days, 95% confidence interval = 8.3–9.2 days) accompanied by mild malaria symptoms. Most frequent symptoms were headache (14 of 15 volunteers) and fever (11 of 15 volunteers). Resolution of symptoms followed after a few days upon chloroquine treatment (Verhage D, unpublished data).
Samples for the real-time quantitative PCR were collected at the same time as blood smears. Figure 2 shows the kinetics of parasitemia of individual volunteers, as determined by the real-time quantitative PCR, until blood smears became positive and chloroquine treatment was initiated. A highly reproducible pattern of increasing parasitemia was evident, with a typical wave-like pattern, attributable to the sequestration of maturing intra-erythrocytic parasites in the peripheral vasculature.11
Table 1 shows the parameters used for the curves in Figure 2, which were based on fitting the statistical model to the data of the quantitative real-time PCR. For all individuals, the observed and expected values match very well, and the goodness of fit does not depend on number of days after infection. The mean estimated number of infected hepatocytes was 207 with a wide range between individuals (29–560). There was a weak association with the number of infected and blood fed mosquitoes (range = 4–7), but no association with the number of red spots on the skin induced by the probing mosquito. The mean pre-patent period, i.e., first appearance of ring forms in the blood, was at 6.83 days (individuals varied from 6.71 to 7.33 days). The mean asexual cycle was 43.7 hours (range = 42.2–45.6 hours), which is the summation of the mean duration of ring forms (1.18 days, 28.3 hours) and mature trophozoites/schizonts (0.64 days, 15.4 hours). The asexual parasite multiplication factor in vivo is estimated to be 7.5 (range = 6.1–9.6).
Using our statistical model, the development of parasitemia can be predicted for volunteers immunized with pre-erythrocytic and/or asexual stage vaccines with different levels of efficacy (Figure 3). Figure 3a shows the efficacy of pre-erythrocytic vaccines with respective reductions of 0%, 70%, 95%, and 99% of infected hepatocytes with subsequent release of merozoites. Clearly, a reduction in the number of hepatocytes leads to a lower initial value, but the pattern of increasing parasitemia thereafter remains unaltered. As a result, even a vaccine with 99% efficacy (red line) only causes a delay of slightly more than two multiplication cycles, that is about four days.
Inhibition of parasite multiplication in individuals vaccinated with asexual vaccines with 0%, 40%, 70%, and 90% efficacy, respectively, is shown in Figure 3b. We assumed that induced immune responses are equally effective against merozoites from liver and from blood stages. While 70% vaccine efficacy permits only a very slow increase in parasite density, 90% efficacy will actually result in a decrease in parasitemia. Given the estimated multiplication rate of 7.5, stable parasitemia is obtained with 86.7% vaccine efficacy (100 × [1 − 1/7.5]). Finally, Figure 3c shows the combination of both pre-erythrocytic and asexual stage vaccines, which is clearly superior to single stage vaccines. Even vaccines with limited efficacy show in combination a synergistic effect on the inhibition of parasitemia, which may be sufficient for clinical protection.
DISCUSSION
In this report, we present a statistical model to determine efficacy of pre-erythrocytic as well as asexual stage malaria vaccines. Our quantitative analyses permit, for the first time, a detailed estimation of critical parameters in the parasite life cycle that are of direct relevance to vaccine evaluation. The model is based on quantitative real-time PCR measurements of parasitemia in non-immune volunteers experimentally infected by P. falciparum-infected mosquitoes. In our model, we explicitly simulated the mechanisms behind increasing (parasite multiplication) and decreasing (sequestration) levels of parasitemia, instead of choosing a more empirical approach. This was possible because repeated individual observations (usually 3–4) were available per multiplication cycle. Our observation of a plateau at the top of every cycle demonstrates that an increasing sine curve, as assumed by others (e.g., Simpson and others12), is not really applicable for describing patterns of parasitemia. The fact that we could achieve a good fit of the data from all individuals suggests a high robustness and validity of our statistical model.
Due to a number of international initiatives, there is a substantial increase in the production of candidate malaria vaccines at clinical grade in preparation for human trials.1 Following successful phase I safety trials, many of these products will qualify for phase II trials, in which the first efficacy studies may be undertaken. In the absence of clear immunologic correlates for protective efficacy, it is difficult to rationally prioritize candidates for product development. Correlate markers of protection that have been used in animal models, or in vitro assays in human studies, often provide equivocal results.13,14 The logical step, therefore, is to test vaccine efficacy in phase IIb trials in malaria-endemic countries. However, few endemic sites are currently available and/or sufficiently equipped, logistics to carry out trials under these conditions are costly and complex, study populations may need to be relatively large to obtain meaningful results, and parameters that assist in evaluation of efficacy such as time of infection cannot be determined. Evaluation of vaccine efficacy by using experimental infection in phase IIa trials has strong added values. Such challenges are relatively cheap, are carried out under safe and controlled conditions, and provide a more solid ethical basis to test the candidate vaccine in endemic countries should protection be found.
Hundreds of experimental infections have been safely and reliably carried out in human volunteers with P. falciparum-infected mosquitoes to test efficacy of pre-erythrocytic vaccines using microscopy for parasite detection.2–4 Results from experimental infections have not been systematically investigated in relation to protection levels from field trials; however, encouraging results were recently obtained with the RTS/S vaccine, where protection obtained in a phase IIa challenge trial was comparable to field data in a subsequent phase IIb study.3,15
This study shows that efficacy of pre-erythrocytic vaccines can be assessed during the incubation period, which reduces discomfort and potential risks associated with disease.
The estimated duration of pre-patent periods is 6.8 days, which is 2–3 days before clinical symptoms occur.16–19 Treatment may be given after the first wave of ring forms (around day 8) to allow for an estimation of the number of infected hepatocytes. In this way, an indication can be obtained of vaccine-induced reductions of the parasite load in the infected liver.
Asexual stage vaccines aim at reductions in parasite multiplication and are more complicated to evaluate by phase IIa trials. Because of the immediate release of tens of thousands of merozoites from infected hepatocyte(s), infections induced by mosquito bite require rapid anti-malarial drug treatment. This has been circumvented by intravenous injection of low numbers of P. falciparum-infected red blood cells and parasite multiplication was measured by PCR.16 Although the number of injected parasites may be standardized, viability of parasites is variable and immunity can be induced by these unphysiologically low doses of asexual parasites.20 In this study, infections were carried out by mosquito bites that represent the physiologic route of infection and allows for potential vaccine effects on merozoites emerging from the liver.
Our quantitative analysis permits, for the first time, a detailed estimation of critical parameters in the in vivo P. falciparum life cycle. With this statistical model, it can be determined which part of the life cycle is affected by an intervention. Some of the estimated life cycle parameters are different from what has been previously published. The mean duration of the in vivo asexual cycle was estimated at 1.82 days (43.7 hours, range = 42.2–45.6 hours). Based on the high quality of our data and model, and the fact that the goodness of fit did not decrease with time since infection, we believe that the generally well accepted value of 48 hours10,12,16,21 per cycle should be adjusted downwards.
Our estimated parasite multiplication rate of 7.5 per cycle of 1.82 days is exactly equal to the value of 8.2 per pre-set cycle of two days estimated by Simpson and others,12 but is lower than in the studies by Gravenor and others22 and Cheng and others.16 These differences are likely due to the isolate of the parasite used.12
In our study, data points for an average of 1.7 multiplication cycles were obtained following the release of liver-stage merozoites into the bloodstream. The model assumes that multiplication rates, as determined from the relative difference between the second and the first peak, are fixed in malaria-naive volunteers. For example, due to development of immunity, the multiplication rate will at some point decrease, but this is not likely to have occurred during the limited period of several days in our experiments. The quality of the estimates may further improve by additional sampling in the second cycle or during the third peak. Alternatively, treatment of volunteers may be delayed for an additional 48 hours to allow for one additional cycle; such a delay was well tolerated with support of symptomatic treatment as observed in our experiment 2. In other studies, volunteers were allowed to have symptoms as long as tolerated with a parasitemia beyond 107/ml.23 In vaccinees with some level of protection, observation periods may be extended because parasite multiplication is expected to be lower. For example, a person with a 70% effective asexual stage vaccine will, after four cycles, still have levels of parasites below those in non-vaccinated individuals in the second cycle (Figure 3).
Explorations with the model show the expected effect of different levels of vaccine efficacy on parasitemia. It is obvious that pre-erythrocytic vaccines need to be much more efficient than asexual stage vaccines, where effect is obtained in every subsequent multiplication cycle. The model shows that stage-specific vaccines with limited efficacy can be highly efficacious in combination, which is good news.
In conclusion, usage of the real-time quantitative PCR and our statistical model significantly adds to the information that can be obtained from experimental human infections and strengthens the potential of clinical phase IIa studies for evaluation of candidate malaria vaccines before going into field trials.
Estimated parameter values after fitting the model to the data*
| Parameter | Symbol | Value | 95% CI |
|---|---|---|---|
| * Variances in duration are between parasites within persons. CI = confidence interval; exp. = experiment. | |||
| † Estimated for each individual separately. The value of X in the table is the average of the following individual estimates: 29, 31, 221, 373, 359 (exp. 1); 89, 297, 402, 560, 98 (exp. 2); and 30, 232, 102, 112, 178 (exp. 3). | |||
| § Estimated for each individual separately. The value μ1 of in the table is the average of the following individual estimates (in the same order as X above): 6.76, 6.82, 6.67, 6.67, 6.71 (exp. 1); 6.66, 6.84, 7.02, 6.72, 6.95 (exp. 2); and 6.82, 6.98, 6.73, 7.33, 6.77 (exp. 3). | |||
| Number of infected hepatocytes (releasing merozoites) | X | 207 | † |
| Number of ring forms per infected hepatocyte per milliliter of blood | β1 | 6.0 | ‡ |
| Mean duration until appearance of first-generation ring forms (days); pre-patent period | μ1 | 6.83 | § |
| Mean duration until disappearance of ring forms (days) | μ2 | 1.18 | 1.00, 1.35 |
| Mean duration until appearance of a new generation of ring forms (days) | μ3 | 0.64 | 0.53, 0.79 |
| Variance in duration until first appearance of ring forms (days2) | σ12 | 0.030 | 0.023, 0.048 |
| Variance in duration until disappearance of ring forms, variation in duration until appearance of a new generation of ring forms (days2) | σ22, σ32 | 0.004 | −0.002, 0.011 |
| Multiplication factor relating the maximum number of ring forms of one cycle to the previous cycle. | β2 | 7.5 | 6.1, 9.6 |
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 71, 2; 10.4269/ajtmh.2004.71.2.0700196
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 71, 2; 10.4269/ajtmh.2004.71.2.0700196
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 71, 2; 10.4269/ajtmh.2004.71.2.0700196
Observed and predicted parasite densities of 15 individuals experimentally infected with Plasmodium falciparum (Pf) in three experiments each with five volunteers. Markers represent observed number of parasites per milliliter of blood based on the quantitative real-time polymerase chain reaction results. Observations of each individual have the same color. Individual observations in experiments 1 and 3 were continued until a standard blood smear was found positive, after which immediate treatment was provided. In experiment 2, treatment was delayed 48 hours after a positive blood smear, so that 4–5 additional observations were available per volunteer. The best fitting curve for each individual is represented in the same color as the corresponding markers. Table 1 gives the parameter values of the statistical model used for fitting the curves. This figure appers in color at www.ajtmh.org
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 71, 2; 10.4269/ajtmh.2004.71.2.0700196
Observed and predicted parasite densities of 15 individuals experimentally infected with Plasmodium falciparum (Pf) in three experiments each with five volunteers. Markers represent observed number of parasites per milliliter of blood based on the quantitative real-time polymerase chain reaction results. Observations of each individual have the same color. Individual observations in experiments 1 and 3 were continued until a standard blood smear was found positive, after which immediate treatment was provided. In experiment 2, treatment was delayed 48 hours after a positive blood smear, so that 4–5 additional observations were available per volunteer. The best fitting curve for each individual is represented in the same color as the corresponding markers. Table 1 gives the parameter values of the statistical model used for fitting the curves. This figure appers in color at www.ajtmh.org
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 71, 2; 10.4269/ajtmh.2004.71.2.0700196
Observed and predicted parasite densities of 15 individuals experimentally infected with Plasmodium falciparum (Pf) in three experiments each with five volunteers. Markers represent observed number of parasites per milliliter of blood based on the quantitative real-time polymerase chain reaction results. Observations of each individual have the same color. Individual observations in experiments 1 and 3 were continued until a standard blood smear was found positive, after which immediate treatment was provided. In experiment 2, treatment was delayed 48 hours after a positive blood smear, so that 4–5 additional observations were available per volunteer. The best fitting curve for each individual is represented in the same color as the corresponding markers. Table 1 gives the parameter values of the statistical model used for fitting the curves. This figure appers in color at www.ajtmh.org
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 71, 2; 10.4269/ajtmh.2004.71.2.0700196
Predicted parasite densities for an individual with 200 infected hepatocytes and a pre-patent period of 6.8 days in the case of using (a) a pre-erythrocytic vaccine, (b) a-sexual stage vaccine, or (c) a combination vaccine with different degrees of efficacy. The simulated effect of the pre-erythrocyte vaccine was 0% (dark blue line), 70% (yellow), 95% (light blue), and 99% (red). The simulated effect of the asexual-stage vaccine was 0% (dark blue line), 40% (yellow), 70% (light blue), and 90% (red). The effect of combination vaccines was simulated by using a combination of a strong 99% effect on liver stages and a weak 40% effect on asexual stages (yellow line), and a combination of a weak 70% effect on liver stages and a strong 90% effect on asexual stages (red line). Table 1 shows the parameter values of the statistical model used for making the predictions. Pf = Plasmodium falciparum. This figure appers in color at www.ajtmh.org
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 71, 2; 10.4269/ajtmh.2004.71.2.0700196
Predicted parasite densities for an individual with 200 infected hepatocytes and a pre-patent period of 6.8 days in the case of using (a) a pre-erythrocytic vaccine, (b) a-sexual stage vaccine, or (c) a combination vaccine with different degrees of efficacy. The simulated effect of the pre-erythrocyte vaccine was 0% (dark blue line), 70% (yellow), 95% (light blue), and 99% (red). The simulated effect of the asexual-stage vaccine was 0% (dark blue line), 40% (yellow), 70% (light blue), and 90% (red). The effect of combination vaccines was simulated by using a combination of a strong 99% effect on liver stages and a weak 40% effect on asexual stages (yellow line), and a combination of a weak 70% effect on liver stages and a strong 90% effect on asexual stages (red line). Table 1 shows the parameter values of the statistical model used for making the predictions. Pf = Plasmodium falciparum. This figure appers in color at www.ajtmh.org
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 71, 2; 10.4269/ajtmh.2004.71.2.0700196
Predicted parasite densities for an individual with 200 infected hepatocytes and a pre-patent period of 6.8 days in the case of using (a) a pre-erythrocytic vaccine, (b) a-sexual stage vaccine, or (c) a combination vaccine with different degrees of efficacy. The simulated effect of the pre-erythrocyte vaccine was 0% (dark blue line), 70% (yellow), 95% (light blue), and 99% (red). The simulated effect of the asexual-stage vaccine was 0% (dark blue line), 40% (yellow), 70% (light blue), and 90% (red). The effect of combination vaccines was simulated by using a combination of a strong 99% effect on liver stages and a weak 40% effect on asexual stages (yellow line), and a combination of a weak 70% effect on liver stages and a strong 90% effect on asexual stages (red line). Table 1 shows the parameter values of the statistical model used for making the predictions. Pf = Plasmodium falciparum. This figure appers in color at www.ajtmh.org
Citation: The American Journal of Tropical Medicine and Hygiene Am J Trop Med Hyg 71, 2; 10.4269/ajtmh.2004.71.2.0700196
Authors’ addresses: Cornelus C. Hermsen, Geert Jan A. van Gemert, Denise S. C. Telgt, and Robert W. Sauerwein, Department of Medical Microbiology 188, University Medical Center Nijmegen, PO Box 9101, 6500 HB Nijmegen, The Netherlands, Telephone: 31-24-361-3663, Fax: 31-24-361-4666, E-mails: r.hermsen@ncmls.kun.nl, g.vangemert@mmb.umcn.nl, d.telgt@aig.umcn.nl, and r.sauerwein@mmb.umcn.nl. Sake J. de Vlas, Department of Public Health, Erasmus Medical Center, University Medical Center Rotterdam, PO Box 1738, 3000 DR Rotterdam, The Netherlands, Telephone: 31-10-408-7985/8285, Fax: 31-10-408-9449, E-mail: s.devlas@erasmusmc.nl. Danielle F. Verhage, Department of Internal Medicine 541, University Medical Center Nijmegen, PO Box 9101, 6500 HB Nijmegen, The Netherlands, E-mail: d.verhage@aig.umcn.nl.
Acknowledgments: We thank M. van de Vegte-Bolmer for culturing malaria parasites, T. Arens and M. Sieben for skilled microscopy, J. van der Meer for clinical assistance, N. Nagelkerke for statistical advice, and W. Eling and A. Thomas for critical review and discussions.
Financial support: This project was supported by the European Union FP 5, contract number QLK2 -CT-1999-01293.
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