Mathematical Model of the Dynamics of Corruption Considering Losing Immunity of Ex - Convict

Abstract

In this study, a mathematical model was developed to describe the dynamics of corruption using an epidemiological modelling approach, considering the loss of immunity of ex-convicts. The population is divided into five compartments consisting of susceptible S(t), Exposed E(t), Corrupt C(t), Jailed J(t) and Reformed R(t). The model’s equilibria are identified, and the stability of these equilibria is studied in depth. At the corruption free equilibrium point (CFEP), the next-generation matrix technique is used to estimate the corruption reproduction number R₀. The CFEP is stable when R₀ <1, however, when R₀ >1, then corruption would persist in society. Furthermore, the sensitivity of the model parameters was investigated, and recommendations were made. Lastly, a numerical solution was performed to confirm the analytical solutions.