The explicit series solution of SIR and SIS epidemic models.

*(English)*Zbl 1171.92033Summary: 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 is 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.

##### MSC:

92D30 | Epidemiology |

37N25 | Dynamical systems in biology |

34A34 | Nonlinear ordinary differential equations and systems, general theory |

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\textit{H. Khan} et al., Appl. Math. Comput. 215, No. 2, 653--669 (2009; Zbl 1171.92033)

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