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

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.