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. / 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.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/17649 |
| Date | 06 May 2015 |
| Creators | Mwamtobe, Peter Mpasho Mwamusaku |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf, application/pdf |
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