Mathematical modelling of the in-host dynamics of malaria and the effects of treatment


Authors

Zadoki Tabo - Department of Mathematics, Makerere University, Kampala, P. O. Box 7062, Uganda.
Livingstone S. Luboobi - Department of Mathematics, Makerere University, Kampala, P. O. Box 7062, Uganda.
Joseph Ssebuliba - Department of Mathematics, Makerere University, Kampala, P. O. Box 7062, Uganda.


Abstract

Malaria research and mathematical models have mainly concentrated on malaria Plasmodium at the blood stage. This has left many questions concerning models of parasite dynamics in the liver and within the mosquito. These concerns are anticipated to keep scientists busy trying to understand the biology of the parasite for some more years to come. Thorough knowledge of parasite biology helps in designing appropriate drugs targeting particular stages of Plasmodium. To achieve this, there is need to study the transmission dynamics of malaria and the interaction between the infection in the liver, blood and mosquito using a mathematical model. In this study, a within-host mathematical model is proposed and considers the dynamics of P. falciparum malaria from the liver to the blood in the human host and then to the mosquito. Several techniques, including center manifold theory and sensitivity analysis are used to understand relevant features of the model dynamics like basic reproduction number, local and global stability of the disease-free equilibrium and conditions for existence of the endemic equilibrium. Results indicate that the infection rate of merozoites, the rate of sexual reproduction in gametocytes, burst size of both hepatocytes and erythrocytes are more sensitive parameters for the onset of the disease. However, a treatment strategy using highly effective drugs against such parameters can reduce on malaria progression and control the disease. Numerical simulations show that drugs with an efficacy above 90% boost healthy cells, reduce infected cells and clear parasites in human host. Therefore more needs to be done such as research in parasite biology and using highly effective drugs for treatment of malaria.


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