Optimal (control of) intervention strategies for malaria epidemic in Karonga district, Malawi

Mwamtobe, Peter Mpasho Mwamusaku
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Malaria is a public health problem for more than 2 billion people globally. About 219 million cases of malaria occur worldwide and 660, 000 people die, most (91%) in the African region despite decades of efforts to control the disease. Although the disease is preventable, it is life-threatening and parasitically transmitted by the bite of the female Anopheles mosquito. A deterministic mathematical model with intervention strategies is developed in order to investigate the effectiveness, optimal control and cost effectiveness of Indoor Residual Spraying (IRS), Insecticide Treated Nets (ITNs) and treatment on the transmission dynamics of malaria in Karonga District, Malawi. The effective reproduction number is analytically computed, and existence and stability conditions of the equilibria are explored. The model does not exhibit backward bifurcation. A structured questionnaire was developed, a one-toone interview with a randomly sampled set of individuals conducted to assess the knowledge level of inhabitants of Karonga district about the disease in general and their awareness and application of the intervention strategies. Applying Pontryagin’s Maximum Principle which uses both the Langragian and Hamiltonian principles with respect to a constant time dependent, we derive the necessary conditions for the optimal control of the disease. An economic evaluation of the strategies is carried out by performing a cost-effectiveness analysis to determine the most cost-effective combination of the three intervention measures. The incremental cost-effectiveness ratio (ICER) is calculated in order to compare the costs and effectiveness of all the possible combinations of the three measures. The results show that the combination of treatment, ITNs and IRS is the most cost-effective combination strategy for malaria control. Numerical simulations indicate that the prevention strategies lead to the reduction of both the mosquito population and infected human individuals. Effective treatment consolidates the prevention strategies. Thus, malaria can be eradicated by deployment of combined strategies such as vector control via ITNs and IRS complemented with timely treatment of infected people.
A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. December 2, 2014.