A mathematical model to control the spread of malaria in Ghana

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Malaria is a serious health problem in Ghana and is reported by the Ministry of Health to be responsible for more than 44 percent of outpatient visits and approximately 22 percent of deaths in children under the age of five, which means there is a lot of work to be done if the country wants to achieve the goals set by Roll Back Malaria Partnership (RBM), a global initiative that coordinates actions against malaria. The goal of this thesis is to use clinical malaria data from Ghana Health Service to develop a mathematical model to help control the spread of malaria in Ghana in order to perhaps meet the target year given by RBM programme. The model consists of seven non-linear differential equations which describe the dynamics of malaria with 4 variables for humans and 3 variables for mosquitoes. We perform stability analysis of the model and the next generation method is used to derive the basic reproduction number 〖 R〗_0. We have proved that the disease-free equilibrium is locally asymptotically stable if〖 R〗_0<1 and unstable when 〖 R〗_0>1 . The Centre Manifold theorem is used to show that the model has a unique endemic equilibrium which is locally asymptotically stable when 〖 R〗_0<1 . The basic reproduction number for Ghana is found to be R_0=0.8939 . Numerical simulation of the model suggests that the most effective strategy for controlling or eradicating malaria is to combine the use of insecticide-treated bed nets, indoor residual spraying and chemotherapy, but the best strategy is to reduce the biting rate of the female anopheles mosquito through the use of insecticide-treated bed nets and indoor residual spraying since the malaria parasite has developed resistance to some of the antimalarial drugs.
A Thesis submitted to the School of Graduate Studies, Kwame Nkrumah University of Science and Technology, Kumasi in partial fulfillment of the requirements for the degree of Master of Philosophy in Mathematics, June-2012