Sensitivity and bifurcation analysis of corruption dynamics model with control measures

Abstract

Corruption is an old and complex phenomenon that affects many countries in different forms. Despite many countries using various techniques to control corruption transmission, the problem is still present. Hence, we developed and analyzed a nonlinear deterministic mathematical model that explains the dynamics of corruption to investigate the effect of control measures on the transmission of corruption. Depending on the corruption status we classified the total population into five compartments, which is an extension of the SCJH model, and techniques of reducing corruption transmission were also examined. We have computed the basic reproduction number [Formula: see text] of the model by using the next-generation matrix method and analyzed the stability of the equilibrium point. The stability analysis reveals that corruption-free equilibrium (CFE) is both locally and globally asymptotically stable for [Formula: see text], but the corruption-endemic equilibrium (CEE) is both locally and globally stable for [Formula: see text]. In the model, we established a sufficient condition for the presence of forward bifurcation. We used the normalized forward sensitivity approach to compute the most sensitive parameters that reduce the spread of corruption. The model was simulated by using ode45 code in MATLAB and results indicate that the effective transmission contact rate [Formula: see text] and taking of adequate penalties rate [Formula: see text] reduce corruption. Therefore, this study recommends that reducing the effective transmission contact rate and taking adequate penalty rate were better strategies to reduce the spread of corruption.