Title
The explicit series solution of SIR and SIS epidemic models
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
ISSN
0096-3003
Recommended Citation
"The explicit series solution of SIR and SIS epidemic models" (2009). Faculty Bibliography 2000s. 1723.
https://stars.library.ucf.edu/facultybib2000/1723