Plasmodium falciparum parasitaemia described by a new mathematical model

Department of Medical Biometry, University of Tübingen, Germany.
Parasitology (Impact Factor: 2.56). 05/2001; 122(Pt 4):379-91. DOI: 10.1017/S0031182001007533
Source: PubMed


A new mathematical model of Plasmodium falciparum asexual parasitaemia is formulated and fitted to 35 malaria therapy cases making a spontaneous recovery after primary inoculation. Observed and simulated case-histories are compared with respect to 9 descriptive statistics. The simulated courses of parasitaemia are more realistic than any previously published. The model uses a discrete time-step of 2 days. Its realistic behaviour was achieved by the following combination of features (i) intra-clonal antigenic variation, (ii) large variations of the variants' baseline growth rate, depending on both variant and case, (iii) innate autoregulation of the asexual parasite density, variable among cases, (iv) acquired variant-specific immunity and (v) acquired variant-transcending immunity, variable among cases. Aspects of the model's internal behaviour, concerning variant dynamics, as well as the respective contributions of the three control mechanisms (iii) - (v), are displayed. Some implications for pathogenesis and control are discussed.

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Available from: Hans H. Diebner
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    • "While clinically immune cases are frequently asymptomatic or of low clinical virulence, data from malariatherapy studies suggest naïve cases may also have a wide range of clinical virulence ranging from high virulence to asymptomatic [24]. Other studies suggest that asymptomatic malaria is not limited to areas of high transmission where exposure-related immunity is expected to develop [25-27]. "
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    ABSTRACT: Despite a resurgence in control efforts, malaria remains a serious public-health problem, causing millions of deaths each year. One factor that complicates malaria-control efforts is clinical immunity, the acquired immune response that protects individuals from symptoms despite the presence of parasites. Clinical immunity protects individuals against disease, but its effects at the population level are complex. It has been previously suggested that under certain circumstances, malaria is bistable: it can persist, if established, in areas where it would not be able to invade. This phenomenon has important implications for control: in areas where malaria is bistable, if malaria could be eliminated until immunity wanes, it would not be able to re-invade. Here, we formulate an analytically tractable, dynamical model of malaria transmission to explore the possibility that clinical immunity can lead to bistable malaria dynamics. We summarize what is known and unknown about the parameters underlying this simple model, and solve the model to find a criterion that determines under which conditions we expect bistability to occur. We show that bistability can only occur when clinically immune individuals are more "effective" at transmitting malaria than naïve individuals are. We show how this "effectiveness" includes susceptibility, ability to transmit, and duration of infectiousness. We also show that the amount of extra effectiveness necessary depends on the ratio between the duration of infectiousness and the time scale at which immunity is lost. Thus, if the duration of immunity is long, even a small amount of extra transmission effectiveness by clinically immune individuals could lead to bistability. We demonstrate a simple, plausible mechanism by which clinical immunity may be causing bistability in human malaria transmission. We suggest that simple summary parameters - in particular, the relative transmission effectiveness of clinically immune individuals and the time scale at which clinical immunity is lost - are key to determining where and whether bistability is happening. We hope these findings will guide future efforts to measure transmission parameters and to guide malaria control efforts.
    Full-text · Article · Sep 2013 · BMC Infectious Diseases
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    • "Mathematical modelling of malaria made major leaps forward through the Garki Project and the model built to study it [22], as well as modern models for population dynamics which followed [23-27]. In addition to population-level models, recent research has advanced the state of detailed models of the within-host dynamics of Plasmodium falciparum[28-30]. Models have been constructed to study antigenic variation at the single infection level [31,32]. "
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    ABSTRACT: Background The development of parasitological immunity against malaria affects the ability to detect infection, the efficiency of the local human parasite reservoir at infecting mosquitoes, and the response to reintroduction of parasites to previously cleared areas. Observations of similar age-trends in detected prevalence and mean parasitaemia across more than an order-of-magnitude of variation in baseline transmission complicate simple exposure-driven explanations. Methods Mathematical models often employ age-dependent immune factors to match the observed trends, while the present model uses a new detailed mechanistic model of parasite transmission dynamics to explain age-trends through the mechanism of parasite diversity. Illustrative simulations are performed for multiple field sites in Tanzania and Nigeria, and observed age-trends and seasonality in parasite prevalence are recreated in silico, proffering possible mechanistic explanations of the observational data. Results Observed temporal dynamics in measured parasitaemia are recreated for each location and age-prevalence outputs are studied. Increasing population-level diversity in malaria surface antigens delays development of broad parasitological immunity. A local parasite population with high diversity can recreate the observed trends in age-prevalence across more than an order of magnitude of variation in transmission intensities. Conclusions Mechanistic models of human immunity and parasite antigen diversity can recreate the observed temporal patterns for the development of parasitological immunity across a wide range of transmission intensities. This has implications for the distribution of disease burden across the population, the human transmission reservoir, design of elimination campaigns, and development and roll-out of potential vaccines.
    Full-text · Article · Dec 2012 · Malaria Journal
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    • "Among several mathematical models developed for P. falciparum blood infection (e.g. [91] [92] [93]) one model assumes that above a threshold parasite density var expression becomes less tightly controlled [93]. Merrick et al. propose a model in which the severity of disease depends on a degree of host stress response, leading among others to the observed elevated Pfsir2a and Pfsir2b transcripts (and assumes that protein levels are accordingly increased), which in turn contribute to the deregulation of var gene transcription [85]. "
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    Full-text · Article · Aug 2012 · Molecular and Biochemical Parasitology
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