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Investigation of fractional order bacteria dependent disease with the effects of different contact rates

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  • Qu, Haidong
  • Rahman, Mati ur
  • Ahmad, Shabir
  • Riaz, Muhammad Bilal
  • Ibrahim, Muhammaad
  • Saeed, Tareq

Abstract

Bacterial-dependent diseases are the most deadly infections which may lead a patient to death. Nowadays, due to memory and nonlocality, fractional calculus has been used to study various infectious disease models. In this article, the influence of varied contact rates and the non-emigrating populace of the human environment on the transmission of bacteria-infected diseases is investigated using a fractional-order SIS model in the Atangana-Baleanu (AB) sense. Bacterial growth is considered to be logistic, with a linear intrinsic growth rate as a function of infectives. The system existence theory is examined to guarantee that it has at least one and unique solution. The Ulam-Hyres (UH) stability analysis is presented to show that the solution of the given model is stable. A stable numerical technique (Adams-Bashforth) is used to find the approximate solution of the model. The obtained numerical results are depicted through simulations to study the behavior of the different classes of the considered model. The effects of various contact rates are shown through numerical simulations via MATLAB-17.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003794
    DOI: 10.1016/j.chaos.2022.112169
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    References listed on IDEAS

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    1. 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.
    2. Ullah, Ihsan & Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "Investigation of fractional order tuberculosis (TB) model via Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
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    Cited by:

    1. Daşbaşı, Bahatdin, 2023. "Fractional order bacterial infection model with effects of anti-virulence drug and antibiotic," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Xu, Changjin & Liu, Zixin & Pang, Yicheng & Saifullah, Sayed & Inc, Mustafa, 2022. "Oscillatory, crossover behavior and chaos analysis of HIV-1 infection model using piece-wise Atangana–Baleanu fractional operator: Real data approach," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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