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Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis

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  • Berhe, Hailay Weldegiorgis
  • Qureshi, Sania
  • Shaikh, Asif Ali

Abstract

Non-Markovian characteristics, possessing memory effects and hereditary properties, play a vital role when it comes to the transmission dynamics of a disease or an epidemic within human society over the course of time. As a result, non-local operators from the field of fractional calculus are the most suitable choices to comprehend dynamics of the disease transmission. This research study is related with formulation of dysentery diarrhea dynamical nonlinear autonomous model via fractional Caputo differential operator with order τ ∈ (0, 1). Using fixed point theory, its solutions are determined to have properties satisfying existence and uniqueness conditions under the Caputo operator. In addition, the non-negative hyperoctant R+4 is positively invariant region of the proposed fractional dysentery diarrhea model. Biological parameters of the classical and the Caputo fractional model are estimated under nonlinear parameter estimation technique and the optimized value of the fractional order parameter τ in the Caputo dysentery diarrhea model is computed to be 9.995e-01. The sensitivity of the basic reproduction number R0 is thoroughly investigated for the most and the least sensitive parameter. Numerical simulations are found to be in good agreement with real statistical data and the theoretical predictions about the disease.

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  • Berhe, Hailay Weldegiorgis & Qureshi, Sania & Shaikh, Asif Ali, 2020. "Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304874
    DOI: 10.1016/j.chaos.2019.109536
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    References listed on IDEAS

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    1. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    2. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    3. Altaf Khan, Muhammad & Ullah, Saif & Farooq, Muhammad, 2018. "A new fractional model for tuberculosis with relapse via Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 227-238.
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    5. Hailay Weldegiorgis Berhe & Oluwole Daniel Makinde & David Mwangi Theuri, 2019. "Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model," Journal of Applied Mathematics, Hindawi, vol. 2019, pages 1-13, February.
    6. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    7. Atangana, Abdon & Araz, Seda İğret, 2019. "Analysis of a new partial integro-differential equation with mixed fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 257-271.
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    Cited by:

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