Nonlinear mixed effects modeling of gametocyte carriage in patients with uncomplicated malaria

<p>Abstract</p> <p>Background</p> <p>Gametocytes are the sexual form of the malaria parasite and the main agents of transmission. While there are several factors that influence host infectivity, the density of gametocytes appears to be the best single measure that is related to the human host's infectivity to mosquitoes. Despite the obviously important role that gametocytes play in the transmission of malaria and spread of anti-malarial resistance, it is common to estimate gametocyte carriage indirectly based on asexual parasite measurements. The objective of this research was to directly model observed gametocyte densities over time, during the primary infection.</p> <p>Methods</p> <p>Of 447 patients enrolled in sulphadoxine-pyrimethamine therapeutic efficacy studies in South Africa and Mozambique, a subset of 103 patients who had no gametocytes pre-treatment and who had at least three non-zero gametocyte densities over the 42-day follow up period were included in this analysis.</p> <p>Results</p> <p>A variety of different functions were examined. A modified version of the critical exponential function was selected for the final model given its robustness across different datasets and its flexibility in assuming a variety of different shapes. Age, site, initial asexual parasite density (logged to the base 10), and an empirical patient category were the co-variates that were found to improve the model.</p> <p>Conclusions</p> <p>A population nonlinear modeling approach seems promising and produced a flexible function whose estimates were stable across various different datasets. Surprisingly, dihydrofolate reductase and dihydropteroate synthetase mutation prevalence did not enter the model. This is probably related to a lack of power (quintuple mutations n = 12), and informative censoring; treatment failures were withdrawn from the study and given rescue treatment, usually prior to completion of follow up.</p

Optimally timing primaquine treatment to reduce Plasmodium falciparum transmission in low endemicity Thai-Myanmar border populations

<p>Abstract</p> <p>Background</p> <p>Effective malaria control has successfully reduced the malaria burden in many countries, but to eliminate malaria, these countries will need to further improve their control efforts. Here, a malaria control programme was critically evaluated in a very low-endemicity Thai-Myanmar border population, where early detection and prompt treatment have substantially reduced, though not ended, <it>Plasmodium falciparum </it>transmission, in part due to carriage of late-maturing gametocytes that remain post-treatment. To counter this effect, the WHO recommends the use of a single oral dose of primaquine along with an effective blood schizonticide. However, while the effectiveness of primaquine as a gametocidal agent is widely documented, the mismatch between primaquine's short half-life, the long-delay for gametocyte maturation and the proper timing of primaquine administration have not been studied.</p> <p>Methods</p> <p>Mathematical models were constructed to simulate 8-year surveillance data, between 1999 and 2006, of seven villages along the Thai-Myanmar border. A simple model was developed to consider primaquine pharmacokinetics and pharmacodynamics, gametocyte carriage, and infectivity.</p> <p>Results</p> <p>In these populations, transmission intensity is very low, so the <it>P. falciparum </it>parasite rate is strongly linked to imported malaria and to the fraction of cases not treated. Given a 3.6-day half-life of gametocyte, the estimated duration of infectiousness would be reduced by 10 days for every 10-fold reduction in initial gametocyte densities. Infectiousness from mature gametocytes would last two to four weeks and sustain some transmission, depending on the initial parasite densities, but the residual mature gametocytes could be eliminated by primaquine. Because of the short half-life of primaquine (approximately eight hours), it was immediately obvious that with early administration (within three days after an acute attack), primaquine would not be present when mature gametocytes emerged eight days after the appearance of asexual blood-stage parasites. A model of optimal timing suggests that primaquine follow-up approximately eight days after a clinical episode could further reduce the duration of infectiousness from two to four weeks down to a few days. The prospects of malaria elimination would be substantially improved by changing the timing of primaquine administration and combining this with effective detection and management of imported malaria cases. The value of using primaquine to reduce residual gametocyte densities and to reduce malaria transmission was considered in the context of a malaria transmission model; the added benefit of the primaquine follow-up treatment would be relatively large only if a high fraction of patients (>95%) are initially treated with schizonticidal agents.</p> <p>Conclusion</p> <p>Mathematical models have previously identified the long duration of <it>P. falciparum </it>asexual blood-stage infections as a critical point in maintaining malaria transmission, but infectiousness can persist for two to four weeks because of residual populations of mature gametocytes. Simulations from new models suggest that, in areas where a large fraction of malaria cases are treated, curing the asexual parasitaemia in a primary infection, and curing mature gametocyte infections with an eight-day follow-up treatment with primaquine have approximately the same proportional effects on reducing the infectious period. Changing the timing of primaquine administration would, in all likelihood, interrupt transmission in this area with very good health systems and with very low endemicity.</p

Mathematical Modeling of Malaria Infection with Innate and Adaptive Immunity in Individuals and Agent-Based Communities

Background: Agent-based modeling of Plasmodium falciparum infection offers an attractive alternative to the conventional Ross-Macdonald methodology, as it allows simulation of heterogeneous communities subjected to realistic transmission (inoculation patterns). Methodology/Principal Findings: We developed a new, agent based model that accounts for the essential in-host processes: parasite replication and its regulation by innate and adaptive immunity. The model also incorporates a simplified version of antigenic variation by Plasmodium falciparum. We calibrated the model using data from malaria-therapy (MT) studies, and developed a novel calibration procedure that accounts for a deterministic and a pseudo-random component in the observed parasite density patterns. Using the parasite density patterns of 122 MT patients, we generated a large number of calibrated parameters. The resulting data set served as a basis for constructing and simulating heterogeneous agent-based (AB) communities of MT-like hosts. We conducted several numerical experiments subjecting AB communities to realistic inoculation patterns reported from previous field studies, and compared the model output to the observed malaria prevalence in the field. There was overall consistency, supporting the potential of this agent-based methodology to represent transmission in realistic communities. Conclusions/Significance: Our approach represents a novel, convenient and versatile method to model Plasmodiu

Population dynamics of a pathogen: the conundrum of vivax malaria

Building a mathematical model of population dynamics of pathogens within their host involves considerations of factors similar to those in ecology, as pathogens can prey on cells in the host. But within the multicellular host, attacked cell types are integrated with other cellular systems, which in turn intervene in the infection. For example, immune responses attempt to sense and then eliminate or contain pathogens, and homeostatic mechanisms try to compensate for cell loss. This review focuses on modeling applied to malarias, diseases caused by single-cell eukaryote parasites that infect red blood cells, with special concern given to vivax malaria, a disease often thought to be benign (if sometimes incapacitating) because the parasite only attacks a small proportion of red blood cells, the very youngest ones. However, I will use mathematical modeling to argue that depletion of this pool of red blood cells can be disastrous to the host if growth of the parasite is not vigorously check by host immune responses. Also, modeling can elucidate aspects of new field observations that indicate that vivax malaria is more dangerous than previously thought

Quantitative Analysis of Immune Response and Erythropoiesis during Rodent Malarial Infection

Malarial infection is associated with complex immune and erythropoietic responses in the host. A quantitative understanding of these processes is essential to help inform malaria therapy and for the design of effective vaccines. In this study, we use a statistical model-fitting approach to investigate the immune and erythropoietic responses in Plasmodium chabaudi infections of mice. Three mouse phenotypes (wildtype, T-cell-deficient nude mice, and nude mice reconstituted with T-cells taken from wildtype mice) were infected with one of two parasite clones (AS or AJ). Under a Bayesian framework, we use an adaptive population-based Markov chain Monte Carlo method and fit a set of dynamical models to observed data on parasite and red blood cell (RBC) densities. Model fits are compared using Bayes' factors and parameter estimates obtained. We consider three independent immune mechanisms: clearance of parasitised RBCs (pRBC), clearance of unparasitised RBCs (uRBC), and clearance of parasites that burst from RBCs (merozoites). Our results suggest that the immune response of wildtype mice is associated with less destruction of uRBCs, compared to the immune response of nude mice. There is a greater degree of synchronisation between pRBC and uRBC clearance than between either mechanism and merozoite clearance. In all three mouse phenotypes, control of the peak of parasite density is associated with pRBC clearance. In wildtype mice and AS-infected nude mice, control of the peak is also associated with uRBC clearance. Our results suggest that uRBC clearance, rather than RBC infection, is the major determinant of RBC dynamics from approximately day 12 post-innoculation. During the first 2–3 weeks of blood-stage infection, immune-mediated clearance of pRBCs and uRBCs appears to have a much stronger effect than immune-mediated merozoite clearance. Upregulation of erythropoiesis is dependent on mouse phenotype and is greater in wildtype and reconstitited mice. Our study highlights the informative power of statistically rigorous model-fitting techniques in elucidating biological systems