Abstract
In this paper we proposed a Mathematical model of Measles disease dynamics. The Disease Free Equilibrium (DFE) state, Endemic Equilibrium (EE) states and the characteristic equation of the model were obtained. The condition for the stability of the Disease Free equilibrium state was obtained. We analyze the bifurcation of the Disease Free Equilibrium (DFE) and the result of the analysis was presented in a tabular form.
Highlights
Bifurcation theorem is concerned with dynamical systems which contain one or more external parameters and with the manner in which the solution set may undergo structural changes as the parameters are varied
The equilibrium state in the absence of infection is known as Disease Free Equilibrium (DFE) and is such that, y = 0, From (5)
The condition for stability of DFE is that the eigen values λi < 0; i = 1, 2, 3; From (17)
Summary
Bifurcation theorem is concerned with dynamical systems which contain one or more external parameters and with the manner in which the solution set may undergo structural changes as the parameters are varied. Such behaviour is essentially determined by the stability of solutions and the manner in which this may change as the parameters vary [2]. The population is divided into a susceptible, an infectious (and infected), and a recovered class, denoted by S, I and R, respectively.
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