Mathematical Model with Macaque Population for Plasmodium knowlesi Malaria Disease in Sarawak

Ismas, Binti Ismail (2019) Mathematical Model with Macaque Population for Plasmodium knowlesi Malaria Disease in Sarawak. Masters thesis, Universiti Malaysia Sarawak (UNIMAS).

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Abstract

In 2008, Plasmodium knowlesi, a simian malaria parasite, was accepted as the fifth type of Plasmodium that causes malaria in humans. P. knowlesi accounts for more than 50% of malaria cases in Sarawak. In this research, a mathematical model is formulated with the aim of translating the biological processes occurring between mosquito, macaque and humans during the infection of P. knowlesi malaria into a mathematical model. The objectives of this research are to formulate the mathematical model of P. knowlesi malaria that incorporates the macaque population and to estimate the value of basic reproduction number, R_0 for P. knowlesi malaria. This model is formulated by using compartmental model. After the formulation of the model, it is translated into mathematical differential equations based on the Balance Law for simulation purposes. The simulation of the model is then compared with the actual cases in Sarawak. The proposed model is able to capture the number of infected humans reasonably well when compared with the number of actual cases. Besides, the simulation of the model without the macaque population is also presented in this project in order to observe the differences. The analysis of the basic reproduction number, R_0 and the disease free equilibrium are included as part of the analysis. Based on the analysis, the disease free equilibrium is stable which indicates that it is possible for Sarawak to be free of P. knowlesi malaria. An expression for R_0 is presented and the value is calculated to be 1.0118. As the value of $R_0$ is more than 1, this indicates that one infection will be able to spread to slightly one new case. When further analysis was done on the R_0, it turned out that the parameter that is significant in affecting the value of R_0 is the Disease Induced Death Rate for Macaque, u_2. This discovery will be able to help us in planning the control strategies for this disease. As a conclusion, the problem of the increasing numbers of P. knowlesi malaria cases in Sarawak needs to be taken seriously, and essential preventive steps must be in place in order for our nation to achieve the objective of eliminating malaria by the year 2020.

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