Application of Homotopy Analysis Method to SIR Epidemic Model

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Application of Homotopy Analysis Method to SIR Epidemic Model

Author Affiliations

¹Department of Mathematics, Khansar Faculty of Mathematics and Computer Science, University of Isfahan, Isfahan, IRAN
² Department of Mathematics, Khorasgan Branch, Islamic Azad University, Isfahan, IRAN
³ Department of Applied Mathematics, Faculty of Mathematical Sciences,Shahrekord University, Shahrekord, IRAN

Res. J. Recent Sci., Volume 2, Issue (1), Pages 91-96, January,2 (2013)

Abstract

In this article, the problem of the spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic is considered. Mathematical modeling of the problem leads to a system of nonlinear ordinary differential equations. Homotopy analysis method is employed to solve this system of nonlinear ordinary differential equations.

References

Liao S.J., The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, (1992)
Liao S.J., A kind of linear invariance under homotopy and some simple applications of it in mechanics, Bericht Nr. 520. Institute fuer Sciffbau der Universitaet Hamburg, (1992)
Liao S.J., Numerically solving nonlinear problems by the homotopy analysis method, Comput. Mech., 20, 530-540 (1997)
Liao S.J., A kind of approximate solution technique which does not depend upon small parameters (II): an application in fluid mechanics, Int. J. Non-linear Mech., 32, 815-822 (1997)
He J.H., Homotopy perturbation technique, Comput Methods Appl. Mech. Engng., 178, 257-262 (1999)
He J.H., A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Nonlinear Mech., 35(1), 37-43 (2000)
Jordan D.W. and Smith P., Nonlinear Ordinary Differential Equations. third ed, Oxford University Press, (1999)
Liao S.J., Homotopy Analysis Method: A New Analytical Technique for Nonlinear Problems, Commun. Nonlinear Sci. Numer. Simul., 2(2) 95-100 (1997)
Liao S.J., Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman and Hall/CRC Press, London/Boca Raton (2003)

[ref1] Liao S.J., The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, (1992)

[ref2] Liao S.J., A kind of linear invariance under homotopy and some simple applications of it in mechanics, Bericht Nr. 520. Institute fuer Sciffbau der Universitaet Hamburg, (1992)

[ref3] Liao S.J., Numerically solving nonlinear problems by the homotopy analysis method, Comput. Mech., 20, 530-540 (1997)

[ref4] Liao S.J., A kind of approximate solution technique which does not depend upon small parameters (II): an application in fluid mechanics, Int. J. Non-linear Mech., 32, 815-822 (1997)

[ref5] He J.H., Homotopy perturbation technique, Comput Methods Appl. Mech. Engng., 178, 257-262 (1999)

[ref6] He J.H., A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Nonlinear Mech., 35(1), 37-43 (2000)

[ref7] Jordan D.W. and Smith P., Nonlinear Ordinary Differential Equations. third ed, Oxford University Press, (1999)

[ref8] Liao S.J., Homotopy Analysis Method: A New Analytical Technique for Nonlinear Problems, Commun. Nonlinear Sci. Numer. Simul., 2(2) 95-100 (1997)

[ref9] Liao S.J., Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman and Hall/CRC Press, London/Boca Raton (2003)