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Nonlinear Engineering

Modeling and Application

Editor-in-Chief: Nakahie Jazar, Gholamreza

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A New Fractional Modelling on Susceptible-Infected-Recovered Equations with Constant Vaccination Rate

Rajnesh Kumar
  • Faculty of Mathematical and Statistical Science, Shri Ramswaroop Memorial University, Lucknow Deva Road, Lucknow, Uttar Pradesh-225003, India
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/ Sunil Kumar
  • Corresponding author
  • Department of Mathematics, National Institute of Technology, Jamshedpur, 801014, Jharkhand, India
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Published Online: 2013-11-18 | DOI: https://doi.org/10.1515/nleng-2013-0021


In this article, the authors introduce a fractional order SIR model with constant vaccination rate. The SIR model has been used in the modeling of several epidemiological diseases, biology and medical sciences. Qualitative results show that the model has two equilibria; the disease free equilibrium and the endemic equilibrium points. The local stability of the model for fractional order time derivative is analyzed using fractional Routh-Hurwitz stability criterion. The fractional derivative is described in Caputo sense. The results obtained through numerical procedure show that the method is effective and reliable.

Keywords: Fractional SIR model; Caputo derivative; Stability analysis; Adams-Bashforth-Moulton method

About the article

Published Online: 2013-11-18

Published in Print: 2014-03-01

Citation Information: Nonlinear Engineering, Volume 3, Issue 1, Pages 11–19, ISSN (Online) 2192-8010, ISSN (Print) 2192-8029, DOI: https://doi.org/10.1515/nleng-2013-0021.

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