The explicit series solution of SIR and SIS epidemic models

    Authors

    H. Khan; R. N. Mohapatra; K. Vajravelu;S. J. Liao

    Abbreviated Journal Title

    Appl. Math. Comput.

    Keywords

    SIR; SIS; Epidemiology; Series solution; Homotopy analysis method; HOMOTOPY ANALYSIS METHOD; INFECTIOUS-DISEASES; EQUATIONS; FLUID; FLOW; Mathematics, Applied

    Abstract

    In this paper the SIR and SIS epidemic models in biology are solved by means of an analytic technique for nonlinear problems, namely the homotopy analysis method ( HAM). Both of the SIR and SIS models are described by coupled nonlinear differential equations. A one-parameter family of explicit series solutions are obtained for both models. This parameter has no physical meaning but provides us with a simple way to ensure convergent series solutions to the epidemic models. Our analytic results agree well with the numerical ones. This analytic approach is general and can be applied to get convergent series solutions of some other coupled nonlinear differential equations in biology. (C) 2009 Elsevier Inc. All rights reserved.

    Journal Title

    Applied Mathematics and Computation

    Volume

    215

    Issue/Number

    2

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    653

    Last Page

    669

    WOS Identifier

    WOS:000269198600026

    ISSN

    0096-3003

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