Stability and Bifurcation Analysis of a Mathematical Modeling of Measles Incorporating Vitamin A Supplement

Samuel Abu Somma, Ninuola Ifeoluwa Akinwande, Paul Gana, Onah David Ogwumu, Timothy Terfa Ashezua and Felix Yakubu Eguda 

Keywords: Stability, equilibrium, measles, trace-determinant, Lyapunov function


Measles is transmissible disease that is common among children. The death caused by measles among children of five years and below is alarming in spite of the safe and effective vaccine. It has been discovered that Vitamin A Deficiency (VAD) in children increases their chances of measles infection. In this paper, the mathematical model of measles incorporating Vitamin A supplement as treatment was formulated and analyzed. The equilibrium points are obtained and analyzed for stability. Bifurcation and sensitivity analyses were carried out to gain further insight into the spread and control of measles. The stability analysis revealed that Disease Free Equilibrium (DFE) is stable if R0 < 1. The bifurcation analysis revealed forward bifurcation while the sensitivity analysis shows the most sensitive parameters of the model that are responsible for the spread and control of the diseases. The effect of sensitive parameters on Basic Reproduction Number, R0 were presented graphically. Vaccination, recovery and Vitamin A supplement rates have been shown from the graphical presentation as the important parameter that will eradicate the measles from the population while contact and loss of immunity rates have shown that measles will persist in the population. People should be sensitized on the danger of living with infected persons. Government should do more in routine immunization and administration of Vitamin A Supplement.