Stability and Bifurcation Analysis of a Mathematical Modeling of Measles Incorporating Vitamin A Supplement
Keywords:Stability; equilibrium; measles; trace-determinant; Lyapunov function
Measles is a contagious disease that is the main cause of death among young children worldwide. Vitamin A deficiency is a recognized risk factor for severe measles and its supplements have been shown to reduce the number of measles deaths. In this paper, the mathematical model of measles incorporating Vitamin A supplement as treatment was formulated. The Disease Free Equilibrium (DFE) point and Endemic Equilibrium (EE) in terms of force of infection were obtained. The local and global stability of the Disease Free Equilibrium (DFE) were analyzed using Trace – Determinant stability method and Lyapunov function respectively. The local and global stabilities of DFE are asymptotically stable if the basic reproduction number and respectively. Bifurcation and sensitivity analyses were carried out on the model. The bifurcation analysis revealed forward bifurcation. And the sensitivity analysis shows that contact rate is the most sensitive parameter to increase the measles while vaccination rate is the most sensitive parameter that will eradicate measles in the population. The effect of sensitive parameters on Basic Reproduction Number, were presented graphically. Vaccination and recovery rates have been shown from the graphical presentation as the important parameter that will eradicate the measles from the population.
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