Mathematical modelling of the in-host dynamics of malaria and the effects of treatment
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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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ISRP Style
Zadoki Tabo, Livingstone S. Luboobi, Joseph Ssebuliba, Mathematical modelling of the in-host dynamics of malaria and the effects of treatment, Journal of Mathematics and Computer Science, 17 (2017), no. 1, 1-21
AMA Style
Tabo Zadoki, Luboobi Livingstone S., Ssebuliba Joseph, Mathematical modelling of the in-host dynamics of malaria and the effects of treatment. J Math Comput SCI-JM. (2017); 17(1):1-21
Chicago/Turabian Style
Tabo, Zadoki, Luboobi, Livingstone S., Ssebuliba, Joseph. "Mathematical modelling of the in-host dynamics of malaria and the effects of treatment." Journal of Mathematics and Computer Science, 17, no. 1 (2017): 1-21
Keywords
- Malaria
- malaria Plasmodium
- sexual and asexual stages
- stability and sensitivity analysis
- treatment.
MSC
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