May 12, 2025 Journal article Open Access

Tadele Giza

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        <foaf:name>Tadele Giza</foaf:name>
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    <dct:title>Presented in Partial Fulfillment of the Requirement for the Degree of Master's in Applied Mathematics (Mathematical Modeling)</dct:title>
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    <dct:issued rdf:datatype="http://www.w3.org/2001/XMLSchema#gYear">2025</dct:issued>
    <dct:issued rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2025-05-12</dct:issued>
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    <dct:description>&lt;p&gt;The aim of this thesis was to formulate a mathematical model of the Gonorrhea disease that included the best possible control measures. First, we proved with great rigor that the solution to the model is bounded and positive within a given domain. We also obtained a basic reproduction number using the nextgeneration matrix, which is essential for evaluating the dynamics of Gonorrhea. The endemic equilibrium point and the Gonorrhea-free equilibrium of the model equation were found to have both local and global stability. The findings demonstrate that the solution converges to the Gonorrhea-free steady-state if the basic reproduction number is less than one, and this shows that the Gonorrhea-free equilibrium asymptotically stable. A sensitivity analysis of the model equation on the important parameters was carried out to evaluate their effect on the dynamics of Gonorrhea transmission. We utilized the Pontryagin minimum principle to obtain control measures, such as prevention and treatment strategies to reduce infectious transmission and prevention interventions to protect susceptible individuals, and we extended the model to optimal control. Numerical simulations were used to verify the effectiveness of the suggested models, and sensitivity analysis shed light on their robustness. According to our analysis, prevention strategies are more effective at reducing Gonorrhea outbreaks. Numerical simulations ultimately highlight that the best strategy uses a synergistic application.&lt;/p&gt;</dct:description>
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