Analysis of a stochastic model of corruption transmission dynamics with temporary immunity

In this investigation, we developed a deterministic SCHRS mathematical model of corruption transmission dynamics and its extended stochastic model after incorporating stochastic factors and Brownian motion. We presented both model analyses in their respective order. The positivity, invariant region, corruption-free equilibrium point, basic reproduction numbers, both local and global stabilities of corruption-free equilibrium, and endemic equilibrium with their stabilities were discussed. The basic reproduction numbers of both deterministic and stochastic approaches are obtained using the next-generation matrix method and twice Itô's differentiable formula. Sensitivity analyses of the impact of relevant parameters are performed. Furthermore, the outcomes of numerical simulations were presented by comparing the deterministic and stochastic approaches to the model's relevant parameters. We observed that as the rate at which the corrupted population interacts with the susceptible population increases, so does the number of corrupted individuals in the community. Moreover, when individuals recover more through education or punishment, the number of corrupted individuals decreases.