Modelling financial crime population dynamics: optimal control and cost-effectiveness analysis
- 31 Downloads
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.
KeywordsFinancial crime model Crime reproduction number Lyapunov functionals Sensitivity analysis Optimal control measures Cost-effective intervention
The authors express thanks to the editor and anonymous reviewers whose insightful suggestions enhanced the original manuscript.
- 5.Zhao H, Feng Z, Castillo-Chávez C (2014) The dynamics of poverty and crime. J Shangai Normal Univ 43(5):486–495Google Scholar
- 20.LaSalle JP (1976) The stability of dynamical systems. In: Regional conference series in applied mathematics. SIAM, Philadelphia, PaGoogle Scholar
- 35.Alhassan A, Momoh AA, Abdullahi AS, Kadzai MTY (2017) Optimal control strategies and cost effectiveness analysis of a malaria transmission model. Math Theory Model 7(6):123–138Google Scholar