IMPACT OF CORRUPT IMMIGRANT ON THE DYNAMICS OF CORRUPTION IN HUMAN POPULATION: A MATHEMATICAL MODELLING APPROACH
Abstract
This study formulated and analyzed a nonlinear deterministic compartmental model of corruption dynamics that explicitly incorporates the influence of corrupt immigrants on a naive population. The population is divided into six compartments: susceptible, exposed, corrupt, prosecuted, jailed, and honest individuals. The model is shown to be well posed, with a positively invariant and attracting feasible region and non-negative solutions for all time. The corruption reproduction number, , is derived using the next-generation matrix approach. The corruption-free equilibrium is proved locally and globally asymptotically stable when , while the corruption-present equilibrium is proved globally asymptotically stable when using quadratic Lyapunov function. Sensitivity analysis identifies the recruitment, influence, prosecution, and reform rates as the parameters to which is most responsive, with reform exerting the strongest negative effect. Numerical simulations confirm the analytical results and show that the long-run endemic level is independent of the initial conditions. Although the sensitivity index of the corrupt-immigrant parameter is small (+0.0437), the simulations show that corrupt immigrants act as a persistent external source of corruption; neglecting this inflow would understate persistence corruption. The results support a combined strategy weighted toward reform, since rehabilitation, civic education, and moral recovery reduce both peak and endemic corruption and ease the burden on the prison system.
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