Modelling Corruption Dynamics and Its Analysis

Abstract

We propose a mathematical model for corruption by considering awareness created by
anti-corruption and counciling in jail. The model is proved to be both epidemiologically and
mathematically well posed. We shown that all solutions of the model are positive and bounded
with initial conditions in a certain meaningful set. The existence of unique corruption-free
and endemic equilibrium points are investigated and the basic reproduction number is com-
puted. Then we study the local asymptotic stability of these equilibrium points. The analysis
shows that the system has a locally asymptotically stable corruption-free equilibrium point
when the reproduction number is less than one and locally asymptotically stable endemic
equilibrium point for the reproduction number is greater than one. The simulation result
shows the agreement with the analytical results.