The explicit series solution of SIR and SIS epidemic models |
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Authors: | Hina Khan Ram N Mohapatra K Vajravelu SJ Liao |
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Institution: | aState Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030, China;bDepartment of Mathematics, University of Central Florida, Orlando, FL 32816, USA |
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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. |
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Keywords: | SIR SIS Epidemiology Series solution Homotopy analysis method |
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