Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 215, Issue 2, Pages 653-669Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2009.05.051
Keywords
SIR; SIS; Epidemiology; Series solution; Homotopy analysis method
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Funding
- National Natural Science Foundation of China
- State Key Lab of Ocean Engineering
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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.
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