Dynamics of Corruption as a Social Pathogen: A Two-Patch Resource-Competition Model with Endogenous Enforcement and Migration

Abstract

This paper formulates and analyzes a novel compartmental model to study the spatial dynamics of corruption, framed as a pathogenic social strategy within a biological resource-competition framework. The model incorporates a renewable resource, whose scarcity drives the transmission of a corrupt strategy among a population of cooperators. The population is stratified into Cooperators (S), Corruptors (C), and Immunes/Enforcers (I), interacting within and between two connected patches via migration. The model exhibits a resource-dependent transmission rate and predator-prey dynamics between Corruptors and Enforcers. We establish the well-posedness of the coupled two-patch system by proving the positivity and boundedness of solutions. The system exhibits a corruption-free equilibrium, whose local and global stability is determined by patch-specific basic reproduction numbers R0(1) and R0(2) , as well as a system-level reproduction number R0 that incorporates migration. We derive critical migration thresholds where the stability of the corruption-free state changes. Bifurcation analysis reveals the existence of a forward transcritical bifurcation at R0 = 1, implying that reducing the system-level reproduction number below unity is sufficient to eliminate the corrupt strategy even in connected populations. Sensitivity analysis via Partial Rank Correlation Coefficients (PRCC) identifies the most critical parameters influencing R0(i) , providing evidence-based policy insights. Numerical simulations corroborate our analytical findings and explore the impact of asymmetric migration on the persistence of corruption. This work provides a theoretical foundation for understanding corruption through an ecological and spatial lens, highlighting the paramount importance of resource availability, enforcement mechanisms, and cross-border connectivity.