Fauziah, Nurlaily Fatinatul, - (2021) Analisis Kestabilan Dan Strategi Kontrol Optimal Model Matematika Dinamika Korupsi. Skripsi thesis, UNIVERSITAS AIRLANGGA.

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Abstract

The problem of corruption is a serious concern in all countries, more so in the developing countries. Corruption does not affect only one aspect of life. Corruption causes a widespread domino effect on the existence of the nation and state. The dynamics of corruption can be constructed in a mathematical model. The purpose of this thesis is to analyze the equilibrium stability of the mathematical model of corruption dynamics and to apply optimal control variables in the form preventive effort and repressive effort . Based on the results of the model analysis without optimal control, there are two equilibrium points, namely the non-endemic and endemic equilibrium point. The local stability of the equilibrium point and the existence of the endemic equilibrium point depend on the basic reproduction number . The non-endemic equilibrium point is asymptotically stable if fulfills two conditions, there are and , while the endemic equilibrium tends to be asymptotically stable if . In this thesis, the sensitivity analysis of parameters will also be carried out to determine which parameters have the most influence on the model. Furthermore, the problem of control variables in this mathematical model is determined using Pontryagin’s Maximum Principle. Numerical simulation results show that providing control variables in the form preventive effort and repressive effort simultaneously provide more effective results in minimizing the corrupt population at optimal costs.

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