Optimal control of malaria chemotherapy


Magombedze, G; Chiyaka, C; Mukandavire, Z; (2011) Optimal control of malaria chemotherapy. Nonlinear Analysis-Modelling and Control, 16 (4). pp. 415-434. ISSN 1392-5113

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Abstract

We present an intra-host mathematical model of malaria that describes the interaction of the immune system with the blood stage malaria merozoites. The model is modified by incorporating the effects of malaria drugs that target blood stage parasites. The optimal control represents a percentage effect of the chemotherapy of chloroquine in combination with chlorpheniramine on the reproduction of merozoites in erythrocytes. First we maximise the benefit based on the immune cells, and minimise the systemic cost based on the percentage of chemotherapies given and the population of merozoites. An objective functional to minimise merozite reproduction and treatment systemic costs is then built. The existence and uniqueness results for the optimal control arc established. The optimality system is derived and the Runge-Kutta fourth order scheme is used to numerically simulate different therapy efforts. Our results indicate that highly toxic drugs with the compensation of high infection suppression have the potential of yeilding better treatment results than less toxic drugs with less infection suppression potential or high toxic drugs with less infection suppression potential. In addition, we also observed that a treatment protocol with drugs with high adverse effects and with a high potential of merozoite suppression can be beneficial to patients. However, an optimal control strategy that seeks to maximise immune cells has no potential to improve the treatment of blood stage malaria.

Item Type: Article
Keywords: malaria modelling, chroloquine chemotherapy, optimal control, Plasmodium, falciparum, plasmodium-falciparum malaria, hiv/aids model, in-vitro, t-cells, infection, immunity, parasite
Faculty and Department: Faculty of Public Health and Policy > Dept of Global Health and Development
Research Centre: Social and Mathematical Epidemiology (SaME)
SaME Modelling & Economics
Web of Science ID: 299647400004
URI: http://researchonline.lshtm.ac.uk/id/eprint/333695

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