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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 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, Hindawi, vol. 2014, pages 1-9, April.
    • Handle: RePEc:hin:jnlaaa:136263
    DOI: 10.1155/2014/136263
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    Cited by:

    1. Sweilam, N.H. & AL-Mekhlafi, S.M. & Alshomrani, A.S. & Baleanu, D., 2020. "Comparative study for optimal control nonlinear variable-order fractional tumor model," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    2. Chatterjee, Amar Nath & Ahmad, Bashir, 2021. "A fractional-order differential equation model of COVID-19 infection of epithelial cells," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    3. Amar Nath Chatterjee & Fahad Al Basir & Bashir Ahmad & Ahmed Alsaedi, 2022. "A Fractional-Order Compartmental Model of Vaccination for COVID-19 with the Fear Factor," Mathematics, MDPI, vol. 10(9), pages 1-15, April.
    4. Zhang, Yong & Yu, Xiangnan & Sun, HongGuang & Tick, Geoffrey R. & Wei, Wei & Jin, Bin, 2020. "Applicability of time fractional derivative models for simulating the dynamics and mitigation scenarios of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Rihan, F.A. & Al-Mdallal, Q.M. & AlSakaji, H.J. & Hashish, A., 2019. "A fractional-order epidemic model with time-delay and nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 97-105.
    6. Sweilam, N.H. & AL - Mekhlafi, S.M. & Baleanu, D., 2021. "A hybrid stochastic fractional order Coronavirus (2019-nCov) mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    7. Ardak Kashkynbayev & Fathalla A. Rihan, 2021. "Dynamics of Fractional-Order Epidemic Models with General Nonlinear Incidence Rate and Time-Delay," Mathematics, MDPI, vol. 9(15), pages 1-16, August.
    8. Rihan, F.A. & Rajivganthi, C, 2020. "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    9. Qu, Haidong & Rahman, Mati ur & Ahmad, Shabir & Riaz, Muhammad Bilal & Ibrahim, Muhammaad & Saeed, Tareq, 2022. "Investigation of fractional order bacteria dependent disease with the effects of different contact rates," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    10. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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