Modelling financial crime population dynamics: optimal control and cost-effectiveness analysis

Abstract

This work is designed to formulate and analyse a mathematical model for population dynamics of financial crime with optimal control measures. Necessary conditions for the existence and stability of financial crime steady states are derived. The financial crime reproduction number is determined. Based on construction of suitable Lyapunov functionals, crime-free equilibrium point of the formulated model is shown to be globally asymptotically stable when the crime reproduction number is below unity, while a unique crime-present equilibrium is proved to be globally asymptotically stable whenever the crime reproduction number exceeds unity. Sensitivity analysis is carried out to determine the relative importance of model parameters in financial crime spread. Furthermore, optimal control theory is employed to assess the impact of two time-dependent optimal control strategies, including public enlightenment campaign (preventive) and corrective measure, on the financial crime dynamics in a population. The cost-effectiveness analysis is carried out to determine the least costly and most effective strategy of the singular and combined implementations of the intervention strategies, when the available resources to combat the spread of financial crime are limited.