Mathematical analysis of foot and mouth disease with optimal control: a case study of FMD in Namibia.
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Date
2023-06
Authors
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Journal ISSN
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Publisher
Namibia University of Science and Technology
Abstract
This study aims to comprehensively analyse Foot and Mouth Disease (FMD) by formulat ing two mathematical models specifically tailored for confined and unconfined environments
in Namibia. The models composed for this research incorporate essential compartments that
capture the intricate dynamics of livestock populations, including their susceptibility to FMD,
latent exposure, infectiousness, and recovery. Furthermore, the models account for the imple mentation of optimal control measures by farmers and the disease control mechanisms em ployed by national institutions such as the vaccination campaign, culling and quarantining of
livestock.
To ensure the stability and equilibrium of the proposed models, well-established mathemat ical principles such as the LaSalle Invariance principle, Lyapunov function and Routh-Hurwitz
stability analysis are utilized. These methods assist in determining the equilibrium points of
the models and assessing their stability properties. In addition, historical data on FMD reported
cases within the country is also incorporated to enhance the accuracy and applicability of the
models analyses.
The study utilises numerical simulations with an Ordinary Differential Equation (ODE) solver
in Python to demonstrate the impact of various scenarios of FMD progression. Furthermore,
an excel-input data sheet is created to facilitate basic analysis and to showcase the variability
range resulting from modifications in FMD dynamics.
By employing a combination of mathematical modelling, stability analysis, historical data
integration, and numerical simulations, this research provides significant insights into the be haviour and control of FMD in confined and unconfined environments in Namibia. The findings
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contribute to the existing knowledge of FMD in Namibia and provide insights that can inform
decision-making and policy formulation in combating this economically significant disease.
Description
A PROJECT SUBMITTED IN FULFILMENT OF THE REQUIREMENT
FOR THE AWARD OF THE DEGREE OF
MASTER OF SCIENCE (MSc.)
Keywords
Mathematical analysis, Foot and mouth disease, FMD Namibia
Citation
Ndeevelo, P. M. (2023). Mathematical analysis of foot and mouth disease with optimal control: a case study of FMD in Namibia [Unpublished master's thesis]. Namibia University of Science and Technology.