Homotopy Analysis Method for an Epidemic Model

Jafar BIAZAR; Mohammad HOSAMI

Authors

Jafar BIAZAR Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht
Mohammad HOSAMI Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht

Keywords:

Homotopy analysis method, system of nonlinear ordinary differential equations, epidemic model

Abstract

In this paper, Homotopy analysis method (HAM) is employed to solve a system of nonlinear equations. The model is the problem of the spread of a non-fatal disease in a population with a constant size, over the period of the epidemic. Mathematical modeling of the problem leads to a system of nonlinear ordinary differential equations. This system has been solved by HAM. Suitable values of the auxiliary parameter h are determined, using h-curves. Approximate solutions are plotted and also presented in governing on the problem of the epidemic model.

doi:10.14456/WJST.2014.38

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Author Biographies

Jafar BIAZAR, Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht

Department of Applied Mathematics

Mohammad HOSAMI, Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht

Department of Applied Mathematics

References

DW Jordan and P Smith. Nonlinear Ordinary Differential Equations. 3rd ed. Oxford University Press, 1999.

F Brauer and C Castillo-Chávez. Mathematical Models in Population Biology and Epidemiology. Springer, New York, 2001.

J Biazar. Solution of the epidemic model by Adomian decomposition method. Appl. Math. Comput. 2006; 173, 1101-6.

SJ Liao. Beyond Perturbation: Introduction to the Homotopy Analysis Method. CRC Press, Boca Raton, 2003.

RA Van Gorder and K Vajravelu. On the selection of auxiliary functions, operators, and convergence control parameters in the application of the Homotopy Analysis Method to nonlinear differential equations: A general approach. Commun. Nonlinear Sci. Numer. Simulat. 2009; 14, 4078-89.

SJ Liao and KF Cheung. Homotopy analysis of nonlinear progressive waves in deep water. J. Eng. Math. 2003; 45, 105-16.

SJ Liao. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 2004; 147, 499-513.

SJ Liao. Notes on the homotopy analysis method: Some deﬁnitions and theorems. Commun. Nonlinear Sci. Numer. Simulat. 2009; 14, 983-97.

SJ Liao. On the relationship between the homotopy analysis method and Euler transform. Commun. Nonlinear Sci. Numer. Simulat. 2010; 15, 1421-31.

ZM Odibat. A study on the convergence of homotopy analysis method. Appl. Math. Comput. 2010; 217, 782-9.

S Liang and DJ Jeffrey. Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation. Commun. Nonlinear Sci. Numer. Simulat. 2009; 14, 4057-64.

H Zhu, H Shu and M Ding. Numerical solutions of partial differential equations by discrete homotopy analysis method. Appl. Math. Comput. 2010; 216, 3592-605.