Stability and control analysis of an unemployment model incorporating integration programs effect

A new mathematical model is proposed to investigate the mechanisms of unemployment with government interventions such as internships programs. The proposed model consists of a compartmental system of four components, which are the unemployment U, the employment E, the unemployed beneficiaries of government programs Up and the cumulative density of programs P. The qualitative analysis of differential equations is used to analyze the model. First the equilibrium’s states are calculated, then the analysis of their stability is discussed with to help of Routh-Hurwitz criterion and Lyapunov’s method. Furthermore,in order to achieve the effectiveness and performance of government programs an optimal control strategy is introduced, in which two control variables are introduced. Finally, to validate the main analytical results, some numerical investigations are performed. Our findings suggest that, a government’s efforts to increase employment opportunities and assist unemployed people in starting their own businesses are more effective at lowering the unemployment rate. Further, companies should be encouraged to take on the unemployed who have benefited from internship programs