Global stability analysis of an unemployment model with distributed delay

摘要

A mathematical model with distributed time delay describing the labour market is investigated, focusing on the asymptotic stability of the unique positive equilibrium point. The positivity and boundedness of the solutions are proved and the local stability analysis reveals that the positive equilibrium point is asymptotically stable, regardless of the distributed time delay considered in the model. Moreover, the construction of a suitable Lyapunov function leads to global asymptotic stability results. Numerical simulations are presented with the aim of substantiating the theoretical statements.