Approximate analytical solution of the fractional epidemic model
About this article
Abstract
In this paper an analytical expression for the solution of the fractional order epidemic model of a non-fatal disease in a population which is assumed to have a constant size over the period of the epidemic is presented. Homotopy analysis method (HAM) is implemented to give approximate and analytical solutions of the presented problem.
References
[1] J. Biazar, Solution of the epidemic model by Adomian decomposition method, Applied Mathematics and Computation, 173 (2) (2006) 1101–1106.
[2] A.A.M. Arafa, S.Z. Rida and M. Khalil, Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection, Nonlinear Biomedical Physics, 6 ( 2012) 1-7.
[3] Hany N. Hassan, and Magdy A. El-Tawil, A new technique of using homotopy analysis method for solving high-order nonlinear differential equations, Math. Meth. Appl. Sci. 34 (2011) 728–742.
[4] D.W. Jordan, P. Smith, Nonlinear Ordinary Differential Equations, third ed., Oxford University Press, 1999.
[5] Mohammad Zurigat, Shaher Momani, Ahmad Alawneh, Analytical approximate solutions of systems of fractional algebraic differential equations by homotopy analysis method, Computers and Mathematics with Applications 59(2010) 1227–1235.
View more references (6)
[6] Mohammad Zurigat , Shaher Momani , Zaid Odibat , Ahmad Alawneh, The homotopy analysis method for handling systems of fractional differential equations, Applied Mathematical Modelling 34 (2010) 24–35.
[7] M. Rafei, H. Daniali, D.D. Ganji, Variational iteration method for solving the epidemic model and the prey and predator problem, Applied Mathematics and Computation 186 (2007) 1701–1709.
[8] M. Rafei , D.D. Ganji, H. Daniali, Solution of the epidemic model by homotopy perturbation method, Applied Mathematics and Computation, 187 (2007) 1056–1062.
[9] S.J. Liao, Notes on the homotopy analysis method: Some definitions and theorems, Commun Nonlinear Sci Numer Simulat 14 (2009) 983–997.
[10] S.J. Liao, The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems, Ph.D. Thesis, Shanghai Jiao Tong University, 1992.
[11] Zaid Odibat, Shaher Momani , Hang Xu, A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations, Applied Mathematical Modelling 34 (2010) 593-600.