A Stochastic Model for Planning a Compartmental Education System and Determining Stable Student Population Distribution

Abstract

In most developing countries, populations grow exponentially thus directly impacting on student populations in education systems. In an ecosystem, a stable predator/prey population ensures the survival and sustenance of the different species in the food. chain. Likewise, a stable student population distribution in an education system is desirable for the survival of the system, resource planning and also for projecting on future manpower supply from the system. A model that encompasses the different compartments of an education system is developed in this paper. The model clearly shows the transition rates within and between compartments in an education system thus enhancing the understanding of student flows in the system, for better planning of manpower systems. The theory of Absorbing Markov Chains is used and the Chapman-Kolmogorov result assists in predicting the expected number of successful graduates for absorption into the workforce. Further, both the rate of growth of the student population and the stable student population distribution are estimated using PerronFrobenius theorem and Relational Differential Equations.