Abstract

MATHEMATICAL MODELLING OF CORRUPTION: EFFECTS AND CONTROL

Anka G.H.1, Mayaki Z.I.2,Altine M.M.3, and Yusuf I. 4

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Abstract In consideration of human population in a given society and hence we found that corruption has a vital and regrows effect on the social behavior and socio-economic pattern and that it is endemic, cancerous and oracular in nature because it normally catches up with people or community and its spread has a significant effect on the lives of people and can easily engulfs the entire society once its spread from one person to another. In this work we obtain a basic reproduction number which can be used to know the rate of spread of corruption between the susceptible individuals, the exposed, the infected class and hence established the Conditions for local and Global stability of both the Corruption-free Equilibrium(CFE) and Corruption-Endemic Equilibrium(CEE).And The Result shows that corruption dies out of the society whenever , at Corruption-free Equilibrium(CFE) and persist whenever , At Corruption-Endemic Equilibrium(CEE).This work focuses on the effect and control of corruption tested for the existence and uniqueness of solution for the model using the Lipchitz condition to ascertain the efficacy of the model and proceeded to determine both the corruption Free Equilibrium (CFE) and the Corruption Endemic Equilibrium (CEE) for the system of equations. We have seen that the system equations has a Unique solution. The local stability of the (CFE) of the model was obtained using the Variational Matrix Criteria while the stability of (CEE) was analyzed. The reproduction number was calculated and simulated. We demonstrated that the disease will die out, if the basic reproductive numbers for the corruption free equilibrium R0< 1. This is the case of a corruption free state, with no infection in the population. Otherwise the corruption may become endemic if the basic reproductive number R0 is bigger than unity (i.e R0> 1). The basic reproduction number at both the Corruption Free State and the endemic state were obtained and the result shows stability in the Control of corruption as a means of reducing the spread in the society. Keywords: corruption, transmission, effect, control, CFE, CEE.

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