June 6, 2023 Thesis Open Access

Merga Hinkosa Bodena

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    <dct:title>MATHEMATICAL MODELING OF THE TRANSMISSION DYNAMICS OF CORRUPTION WITH CONTROL MEASURES</dct:title>
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    <dct:description>&lt;p&gt;Advisor: Dr. Temesgen Duressa Keno&lt;/p&gt; &lt;p&gt;Abstract&lt;/p&gt; &lt;p&gt;In this study, we proposed a nonlinear deterministic mathematical model of corruption dynamics with optimal control analysis. First, we showed that the solution of the model is both positive and bounded in certain domain. Then we computed a basic reproductive number with respect to the corruption-free equilibrium point using next-generation matrix method. Besides, the Routh-Hurwitz criterion and the Lyapunov function are then used to show that corruption-free equilibrium is both locally and globally stable. Then if the basic reproduction number is less than one, the corruption-free equilibrium point is both locally and globally asymptotically stable; otherwise, an endemic corruption equilibrium occurs. Furthermore, the sensitivity of the model&amp;rsquo;s parameters was tested, and the model shows the forward bifurcation. Moreover, the model is extended to an optimal control model using corruption minimization strategies namely prevention and punishment. Also using Pontryagin&amp;rsquo;s minimum principle we obtain the necessary condition of the optimal control problem. Finally, according to numerical prediction of optimality systems, prevention is the most optimal and least cost strategy for minimization corruption.&lt;/p&gt; &lt;p&gt;Keywords: Corruption dynamics model; Global stability; Optimal control analysis; Costeffectiveness strategies, Numerical simulation.&lt;/p&gt;</dct:description>
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