A model of corruption on higher-order networks with long-time quasi-stationary solutions

Corruption is an old, widespread, and almost always unresolved problem. Different responsible actors propose and put into practice various strategies to counteract it. However, effective measures can only be developed with a clear understanding of the underlying mechanism. Mathematical modeling can help figure out the mechanistic description of the phenomenon, including the role of the agents, their interactions, the global structure, and the properties of the population or society under examination. We propose a general framework aimed at describing and analyzing the dynamics through which corruption spreads. Through a set of differential equations that takes into account the networked nature of any community, our model allows, among others, to study individuals split into any number of classes, representing different propensities toward corruption. We show how, thanks to transition matrices, it is possible to model individuals' tendencies for corrupted behavior. The model also allows us to study the impact of group interactions by considering individuals as part of a higher-order network, namely, a simplicial complex. We show that under different parameter settings, initial conditions, and average degree connectivity, the outputs remain qualitatively unchanged: after a transient phase, the dynamics slows down, and there is a progressive increase in the number of corrupt individuals. We find evidence of long-time quasi-stationary solutions for which the number of corrupt individuals keeps increasing. We give insights on how to detect the ideal time for interventions and on thresholds of initial percentage of nearly incorruptible individuals that guarantee a long-time uncorrupted society.