Analysis of malaria transmission dynamics in human and mosquito populations
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Date
2024
Authors
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Journal ISSN
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Publisher
University of Namibia
Abstract
This mini-thesis presents a deterministic mathematical model for the spread of malaria
in human and mosquito populations. The human population is divided into four com partments while mosquito population is divided into three compartments. Suscepti ble humans can be infected when they are bitten by an infected mosquito, they then
progress through the exposed, infected, recovered before going back to the susceptible
class. Susceptible mosquitoes can be exposed to the disease and once they are exposed,
they can be infected, and remain infected until they die. Basic reproduction number,
R0 was established and used to determine whether the disease dies out or persists in the
population. It was shown that the disease-free equilibrium point is locally asymptoti cally stable when R0 < 1 and unstable when R0 > 1. Quantitative analysis of the model
was carried out to confirm the findings from qualitative analysis. Result obtained indi cate that the findings of quantitative analysis correspond to the findings of qualitative
analysis. It was proven qualitatively that R0 < 1, which corresponds to the results of
the sensitivity analysis, that was carried out quantitatively. It was recommended that
future work can be done to investigate the stability of the endemic equilibrium point
Description
A mini-thesis submitted in partial fulfilment of the requirement for the degree of master of science in applied mathematics
Keywords
Reproduction number, Routh-Hurwitz criterion, Mathematical model, Local stability, Steady states