Mathematical model of the first wave of Plasmodium falciparum asexual parasitemia in non-immune and vaccinated individuals.

We present a dynamic model of the highly pathogenic first wave of Plasmodium falciparum asexual parasitemia in non-immune persons. The model was successfully fitted to malaria therapy data. This required four case-specific parameters: the basic two-day multiplication factor, the time of onset of adaptive immunity, and the effective dose 50 densities for the innate and adaptive immune responses, respectively. All four parameters show large case-dependent variation that is mainly attributable to host factors. According to the model, the maximum value of the first wave is controlled mainly by the innate immune response. We used the model to explore the expected effects of vaccines targeting the parasite's asexual blood stages on the basis of what we consider to be the biologically most plausible assumptions concerning the parameter modifications induced by vaccination. According to our simulations, the benefit of antiparasitic vaccination is strongly host dependent and vaccine efficacy at low immunogenicity is much larger against severe disease than against fever. This has implications for the early testing of the protective efficacy of a vaccine in humans.

An epidemiologic model of severe morbidity and mortality caused by Plasmodium falciparum.

The intensity of Plasmodium falciparum transmission has multifarious and sometimes counter-intuitive effects on age-specific rates of severe morbidity and mortality in endemic areas. This has led to conflicting speculations about the likely impact of malaria control interventions. We propose a quantitative framework to reconcile the various apparently contradictory observations relating morbidity and mortality rates to malaria transmission. Our model considers two sub-categories of severe malaria episodes. These comprise episodes with extremely high parasite densities in hosts with little previous exposure, and acute malaria episodes accompanied by co-morbidity or other risk factors enhancing susceptibility. In addition to direct malaria mortality from severe malaria episodes, the model also considers the enhanced risk of indirect mortality following acute episodes accompanied by co-morbidity after the parasites have been cleared. We fit this model to summaries of field data from endemic areas of Africa, and show that it can account for the observed age- and exposure-specific patterns of pediatric severe malaria and malaria-associated mortality in children. This model will allow us to make predictions of the long-term impact of potential malaria interventions. Predictions for children will be more reliable than those for older people because there is a paucity of epidemiologic studies of adults and adolescents.

Relationship between the entomologic inoculation rate and the force of infection for Plasmodium falciparum malaria.

We propose a stochastic model for the relationship between the entomologic inoculation rate (EIR) for Plasmodium falciparum malaria and the force of infection in endemic areas. The model incorporates effects of increased exposure to mosquito bites as a result of the growth in body surface area with the age of the host, naturally acquired pre-erythrocytic immunity, and the reduction in the proportion of entomologically assessed inoculations leading to infection, as the EIR increases. It is fitted to multiple datasets from field studies of the relationship between malaria infection and the EIR. We propose that this model can account for non-monotonic relationships between the age of the host and the parasite prevalence and incidence of disease. It provides a parsimonious explanation for the faster acquisition of natural immunity in adults than in children exposed to high EIRs. This forms one component of a new stochastic model for the entire transmission cycle of P. falciparum that we have derived to estimate the potential epidemiologic impact of malaria vaccines and other malaria control interventions.

A model for natural immunity to asexual blood stages of Plasmodium falciparum malaria in endemic areas.

Most mathematical models for acquired immunity to Plasmodium falciparum consider effects of immunity on duration of infection and infectiousness, but do not consider the most evident effect of immunity, which is to reduce parasite densities. Few attempts have been made to fit such models to field data. We propose a stochastic simulation model to predict the distributions of P. falciparum parasite densities in endemic areas, in which acquired immunity acts by reducing parasite densities. We have fitted this model to age-specific prevalence and geometric mean densities from settings in Ghana, Nigeria, and Tanzania. The model appears to reproduce reasonably well the parasitologic patterns seen in malariologic surveys in endemic areas and is appropriate for predicting the impact of interventions such as vaccination in the context of continual exposure to P. falciparum.

An epidemiologic model of the incidence of acute illness in Plasmodium falciparum malaria.

We propose a stochastic model for simulating malaria tolerance. The model relates the probability of a clinical attack of malaria to the peripheral parasite densities via a pyrogenic threshold that itself responds dynamically to the parasite load. The parameters of the model have been estimated by fitting it to the relationship between incidence of clinical episodes and the entomologic inoculation rate, using age-specific incidence data from two villages in Senegal and one village in Tanzania. The model reproduces the shifts in age distribution of clinical episodes associated with variation in transmission intensity, and in keeping with the data, predicts a slightly higher lifetime number of episodes in the mesoendemic village of Ndiop than in the holoendemic village of Dielmo. This model provides a parsimonious explanation of counter-intuitive relationships between the overall incidence of clinical malaria and transmission intensity. In contrast to the theory of endemic stability, recently proposed to apply to P. falciparum, it does not assume any intrinsic age dependence in the outcome of infection. This model can be used to explore the consequences for predictions of the effects of different anti-malarial interventions on the incidence of clinical malaria.

Mathematical modeling of the impact of malaria vaccines on the clinical epidemiology and natural history of Plasmodium falciparum malaria: Overview.

We report a major project to develop integrated mathematical models for predicting the epidemiologic and economic effects of malaria vaccines both at the individual and population level. The project has developed models of the within-host dynamics of Plasmodium falciparum that have been fitted to parasite density profiles from malaria therapy patients, and simulations of P. falciparum epidemiology fitted to field malariologic datasets from a large ensemble of settings across Africa. The models provide a unique platform for predicting both the short- and long-term effects of malaria vaccines on the burden of disease, allowing for the temporal dynamics of effects on immunity and transmission. We discuss how the models can be used to obtain robust cost-effectiveness estimates for a wide range of malaria vaccines and vaccination delivery strategies in different eco-epidemiologic settings. This paper outlines for a non-mathematical audience the approach we have taken and its underlying rationale.

The Garki project : research on the epidemiology and control of malaria in the Sudan savanna of West Africa / by L. Molineaux and G. Gramiccia / Le projet Garki : recherches sur l' épidémiologie du paludisme et la lutteantipaludique dans la savane soudanienne de l' Afrique occidentale

Presents and assesses the results of a major longitudinal study on the epidemiology and control of malaria in the Sudan Savanna. The study was designed to collect baseline data on the epidemiology and dynamics of transmission, evaluate the effects of different types of intervention, and develop and test a mathematical model of malaria transmission. Results are presented in chapters covering control operations, entomology, parasitology, immunology, blood genetics, demography, clinical findings, and the testing of the mathematical model. The book concludes with practical advice for the future of malaria control