Abstract:
Te increase in the country’s population attracted the establishment of more schools, both public and private schools, to cater for
the increasing number of students. However, there have been dynamics of students’ population both in public and private schools
through transfer from one category of school to the other, through completion of the learning period, and through dropout due to
unknown reasons which have subjected both the public and private schools to compete in order to maintain a good number of
students. In this work, a modifed Lotka–Volterra model of schools and nonenrolled entities population in the education system is
studied. Private schools and nonenrolled entities play the role of a predator in public schools. Again, public schools and
nonenrolled entities play the role of predators in private schools. Holling type II functional responses have been integrated in the
analysis of the Lotka–Volterra model. Te equilibrium points are established and their stability are determined using the
Routh–Hurwitz criterion and eigenvalue method. Global stability has been done for the positive equilibrium point. Bifurcation is
also done around the positive equilibrium point. Finally, a graphical illustration of various parameter is derived to show their efect
on schools when they are varied. It is revealed that the increase in parameters θ2 , θ3 , and η3 greatly afects the schools population as
they are the ones leading to predation in school. Terefore, proper strategies should be developed to focus on reducing the
mentioned parameters to avoid leading schools’ population to extinct
