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 are 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.
Highlights
Malaria remains a major public health problem in most tropical countries, sub-Saharan Africa
Antibodies are secreted at rate η, this secretion is induced by immune cells and depends on the density of merozoites in the blood, that is as the population of merozoites increase more antibodies will be secreted
Our goal is to maximise the benefit based on the number of immune cells and treatment while minimising the merozoite population and the systemic cost of drug chemotherapy
Summary
Malaria remains a major public health problem in most tropical countries, sub-Saharan Africa. The two main facets of CD4+ T cells that are functionally distinguished by the cytokines they solicit, thats is, (i) Th1-type which mainly induce γ-interferon (IFN-γ), and (ii) Th2-type which induce interlukine-4 (IL-4) and IL-5 Both the Th1 and Th2 responses seem to be required to regulate the infection of humans with P. falciparum malaria. The main thrust of this study is to determine how CQ treatment in combination with CP (or an malaria drug that reduce reproduction of merozoites in parasitised erythocytes) should be initiated, investigate drug percentage usage, and effective treatment in the face of emerging malaria drug resistant strains with aid of a model that incorporates the cellular and humoral immune response mechanisms in an elaborate way.
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