A hybrid fractional-order and neural network model for corruption dynamics using the ABC derivative

Abstract

Corruption can be defined as the misuse of power, of public office, or of authority entrusted to the state for one’s benefit, thus bringing to light the lack of transparency, accountability, and fairness in public and private sectors. In this context, we introduce a fresh compartmental model for corruption dynamics which fully aligns theoretical assumptions to empirical realities. The different individuals are divided into the five compartments, namely, susceptible $S^{\varrho }$, corrupt $C^{\varrho }$, under investigation $P^{\varrho }$, jailed $J^{\varrho }$, and honest $H^{\varrho }$. To introduce memory and lineage effects in the corruption dynamics, the Atangana–Baleanu–Caputo fractional derivative is utilized. Applying the next-generation matrix method, we determine the basic reproduction number $R_0$, which acts as a threshold parameter for the survival of corruption in the system. The case of $R_0<1$ corresponds to the situation where the corruption-free equilibrium enjoys both local and global asymptotic stability, while $R_0>1$ results in the endemic equilibrium (corruption-present) being asymptotically stable. Additionally, the bifurcation analysis is used to expound the parameter-induced transitions in the level of corruption and to pinpoint the main intervention mechanisms. The model now achieves improved predictive accuracy through the implementation of an artificial neural network (ANN) method which operates three distinct scenarios that researchers define as $\text{Case 1}$, $\text{Case 2}$, and $\text{Case 3}$. The ANN accurately models the system behavior and encompasses complex nonlinear traits. The ANN-derived predictions match the numerical simulations conducted with Maple 19 and the Lagrange interpolation technique almost perfectly. The results indicate that anti-corruption measures carefully chosen according to the model can lead to a substantial decrease in corruption thus proving the usefulness of the proposed model for political evaluation and strategy-making.