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A Fractional Order Model for the Transmission Dynamics of Measles with Vaccination

DOI: 10.4236/oalib.1106670, PP. 1-13

Subject Areas: Mathematical Analysis, Ordinary Differential Equation, Dynamical System

Keywords: Measles, Vaccination, Fractional-Order Differential Equations, Equilibrium Points, Stability, Numerical Simulations, Predictor-Corrector Method

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Abstract

In this paper, the fractional order model was adopted to describe the dynamics of measles and to establish how the virus that causes measles is transmitted as well as how to mitigate the conditions that cause the spread. We showed the existence of the equilibrium states. The threshold parameter of the model was evaluated in terms of parameters in the model using the next generation matrix approach. We provided the conditions for the stability of the disease free and the endemic equilibrium points. Also, the stability of the various equilibrium points was studied. Numerical simulations of the model are presented graphically using Adam-Bashforth Method and the results were interpreted. The result also shows that the use of vaccination is the best way to prevent measles outbreak.

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Aguegboh, N. S. , Nwokoye, N. R. , Onyiaji, N. E. , Amanso, O. R. and Oranugo, D. O. (2020). A Fractional Order Model for the Transmission Dynamics of Measles with Vaccination. Open Access Library Journal, 7, e6670. doi: http://dx.doi.org/10.4236/oalib.1106670.

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