Mathematical Modelling and Simulation of Competition for Students’ Population Via Influence And Economic Factors With Holling Type Ii Response

Abstract

The increase in Kenyan population attracted the establishment of more schools, both public schools and private schools. This was due to the need to cater for the increasing number of students being enrolled in schools. Moreover, the dynamics of students’ population both in public schools and private schools have created the changes in the schools’ population. This occurs through transfer from one category of school to the other, through completion of the learning period and through drop out due to unknown reasons. This subjected both the public schools and private schools to compete in order to maintain a good number of students under their custody. In this work, a modified Lotka-Volterra model of schools and non-enrolled entities population in the education system is studied. Private schools and non-enrolled entities play the role of a predator in public schools. Again, public schools and non-enrolled entities play the role of predators in private schools. This study uses integrated Holling type II functional response to analyze the model. Establishment of equilibrium points and their stability are determined using the Routh-Hurwitz criterion and eigenvalue method. Global stability has been done for the positive equilibrium point. Hopf bifurcation is also done around the positive equilibrium point. Data obtained from the Ministry of Education and the sources cited were used to estimate the model parameters. Finally, graphical illustration of various parameter is derived to show their effect on schools when they are varied. The study revealed that the increase in transfer rate from private to non-enrolled, transfer rate from public to non-enrolled and the non-enrolled entity predation on public schools greatly affects the schools’ population as they are the ones leading to predation in school. Therefore, proper strategies should be developed to focus on reducing the parameters that affects the schools’ population adversely to avoid leading schools’ population to extinct.