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On Fractional SIRC Model with Salmonella Bacterial Infection

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  • Fathalla A. Rihan
  • Dumitru Baleanu
  • S. Lakshmanan
  • R. Rakkiyappan

Abstract

We propose a fractional order SIRC epidemic model to describe the dynamics of Salmonella bacterial infection in animal herds. The infection‐free and endemic steady sates, of such model, are asymptotically stable under some conditions. The basic reproduction number ℛ0 is calculated, using next‐generation matrix method, in terms of contact rate, recovery rate, and other parameters in the model. The numerical simulations of the fractional order SIRC model are performed by Caputo’s derivative and using unconditionally stable implicit scheme. The obtained results give insight to the modelers and infectious disease specialists.

Suggested Citation

  • Fathalla A. Rihan & Dumitru Baleanu & S. Lakshmanan & R. Rakkiyappan, 2014. "On Fractional SIRC Model with Salmonella Bacterial Infection," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:136263
    DOI: 10.1155/2014/136263
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    References listed on IDEAS

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    1. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    2. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
    3. Fathalla A. Rihan, 2013. "Numerical Modeling of Fractional-Order Biological Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, August.
    4. Fathalla A. Rihan, 2013. "Numerical Modeling of Fractional‐Order Biological Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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