Mathematical modeling of the unemployment problem in a context of financial crisis

• Published in: Mathematics and computers in simulation Vol. 211; pp. 241 - 262
• Main Authors: Njike-Tchaptchet, Eric Rostand, Tadmon, Calvin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2023
• Subjects: Financial crisis; Lyapunov function; Mathematical modeling; Optimal control; Unemployment; Mathematical modeling; Unemployment; Optimal control; Financial crisis; Lyapunov function
• ISSN: 0378-4754; 1872-7166
• DOI: 10.1016/j.matcom.2023.04.014

In this paper, we formulate a new system of nonlinear ordinary differential equations to study the unemployment problem in a context of financial crisis. We first prove the existence of a unique positive equilibrium. Then, using an appropriate Lyapunov function under some specified conditions, we prove the global stability of the unique positive equilibrium. We also propose and compare two control strategies with the objective to improve, at the lowest cost, the employment rate. Our results suggest that, in order to reduce the unemployment rate, it is better for a government to assist unemployed people in building their own business which will allow them to further create new vacancies than to assist self-employed individuals to create new vacancies. Numerical simulations are presented to substantiate the theoretical results. •We propose a new model to study the unemployment problem in financial crisis context.•We prove the global asymptotic stability of the unique equilibrium.•We propose two control strategies to improve, at lowest cost, the employment rate.•We perform numerical simulations to illustrate the theoretical results obtained.