Khalil, M.A.M. Arafa, A.Z. Rida, S.2019-10-192019-10-192012[1] A. Yıldırım, Y. Cherruault, Analytical approximate solution of a SIR epidemic model with constant vaccination strategy by homotopy perturbation method, Emerald 38, 1566 (2009). [2] O.D. Makinde, Adomian decomposition approach to a SIR epidemic model with constant vaccination strategy App. Math. comput., 184, 842 (2007). [3] A.A.M Arafa, S.Z. Rida, M. Khalil, Fractional modeling dynamics of HIV and 4 T-cells during [4] primary infection, Nonlinear biomedical physics, 6 (2012) 1-7. [5] J. Biazar, Solution of the epidemic model by Adomian decomposition method, App. Math. comput., 173 (2) (2006) 1101–1106.App. Math. comput., 173, 1101 (2006). [6] S. Busenberg, P. Driessche, Analysis of a disease transmission model in a population with varying size, J. Math. Biol. 28, 257 (1990). [7] A.M.A. El-Sayed, S.Z. Rida, A.A.M. Arafa, On the Solutions of Time-fractional Bacterial Chemotaxis in a Diffusion Gradient Chamber International Journal of Nonlinear Science, 7, 485 (2009). [8] H. N. Hassan and M. A. El-Tawil, A new technique of using homotopy analysis method for solving high-order nonlinear differential equations, Mathematical methods in applied science. 34(2011) 728–742. [9] S.J. Liao, A kind of approximate solution technique which does not depend upon small parameters: a special example, Int. J. Non-Linear Mech. 30(1995) 371–380. [10] S.J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall/CRC Press, Boca Raton, 2003.https://t.ly/6MBxBChildhood vaccination programs have had a dramatic impact on child morbidity and mortality. Protecting children from diseases that can be prevented by vaccination is a primary goal of health administrators. A SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is presented in this paper. We introduce fractional-order into the presented model. Homotopy analysis method (HAM) is considered in this paper to obtain an analytic approximate solution of this model. The results obtained by HAM are compared with the classical fourth order Runge–Kutta method (RK4) to gauge its effectiveness. The obtained results proved that the disease will persist within the population if the vaccination coverage level is below a certain threshold.enUniversity for Infectious diseases modesFractional order differential equationsHomotopy analysis methodArticle