A mathematical model of unemployment with the effect of limited jobs

Abstract

In this paper, we have proposed and analyzed a non-linear mathematical model of the issue of unemployment by considering three main variables, namely the numbers of unemployed, employed and available vacancies. The model resembles the situation in some countries where the support of the government reaches a certain limited level where the rate of creating new jobs becomes constant and can no longer be proportional to the number of unemployed due to limited financial and economics resources. The qualitative results for the mathematical model are obtained utilizing the stability theory of nonlinear differential equations. Furthermore, some numerical simulations are illustrated to support the qualitative results.