Unemployment remains a major challenge in many developing countries in the world, including Kenya. It is worthy noting that, youths unemployment rate is high and mismatch of skills in the job market is phenomenal. This paper develops a deterministic mathematical model to assess the role of post-secondary education on the unemployment problem in Kenya. We perform a thorough quantitative and qualitative analysis of the model. We compute the unemployment reproduction R u , prove that the model has a unique unemployment free equilibrium (UFE) when R u < 1 and admits a unique unemployment endemic equilibrium (UEE) whenever R u > 1 . The unique UFE and UEE are both locally and globally asymptotically stable whenever R u < 1 and R u > 1 respectively. Further, we validate the model by fitting it to real data of unemployed persons in Kenya in the year 1991−2023 as reported by the International Labour Organization (ILO). Numerical results indicate that, an increased individual’s skills match to the job market demands, significantly decreases the number of unemployed persons and increases the number of employed individuals. Moreover, it is demonstrated that, increasing the rate of employment to the unemployed persons reduces the problem of unemployment substantially. This can be achieved by setting up more sectors for job opportunities.