Mathematical model of unemployment with a cyclical component

In this paper, we proposed and analyzed a new mathematical model of unemployment. Two types of unemployment are involved, structural and cyclical unemployment. The problem is modeled using a nonlinear of ordinary differential system. Three variables are considered, the structural unemployment (S), the employment (E) and the cyclical unemployment (C). Existence, positivity and boundedness of this model are proved. Local stability and global stability are established. The impact of different values of the parameters is analyzed by discussing their sensibility. Numerical simulations are given to confirm the main theoretical findings.