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Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data

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  • Qureshi, Sania
  • Bonyah, Ebenezer
  • Shaikh, Asif Ali

Abstract

This paper is all about the development and analysis of an epidemiological model related to the disease of diarrhea that occurred in Ghana during 2008–2015. Using real statistical data, three new fractional-order mathematical models have been developed on the basis of having information about existing classical model . The new models are formulated with Caputo, Caputo–Fabrizio–Caputo and the Atangana–Baleanu–Caputo fractional-order approaches while taking care of the dimensional analysis during the process of fractionalization. Besides, existence and uniqueness for the solutions of the fractional-order models under each case are proved with the help of fixed point theory whereas positivity and boundedness of models’ solution are also investigated. Steady-states (disease-free and endemic equilibria) points of the model and sensitivity of the basic reproductive number (R0) are also explored. While many of the model’s parameters are fixed, the transmission rate (β) of the disease has been estimated and so is the case with orders of the fractional models. Using minimum distance approach, it has been found that the diarrhea model under investigation estimates the real statistical data well enough when considered with the Atangana–Baleanu–Caputo fractional order operator which has non-local and non-singular kernel. Thus, this fractional-order operator of Atangana–Baleanu in the present research study for the diarrhea model outperforms those having index law, power law and stretched exponential kernels.

Suggested Citation

  • Qureshi, Sania & Bonyah, Ebenezer & Shaikh, Asif Ali, 2019. "Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    • Handle: RePEc:eee:phsmap:v:535:y:2019:i:c:s0378437119314311
    DOI: 10.1016/j.physa.2019.122496
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    1. Mustapha, Umar Tasiu & Qureshi, Sania & Yusuf, Abdullahi & Hincal, Evren, 2020. "Fractional modeling for the spread of Hookworm infection under Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    2. Qureshi, Sania & Memon, Zaib-un-Nisa, 2020. "Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Qureshi, Sania, 2020. "Real life application of Caputo fractional derivative for measles epidemiological autonomous dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Asamoah, Joshua Kiddy K. & Okyere, Eric & Yankson, Ernest & Opoku, Alex Akwasi & Adom-Konadu, Agnes & Acheampong, Edward & Arthur, Yarhands Dissou, 2022. "Non-fractional and fractional mathematical analysis and simulations for Q fever," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    5. Sekerci, Yadigar & Ozarslan, Ramazan, 2020. "Respiration Effect on Plankton–Oxygen Dynamics in view of non-singular time fractional derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    6. Qureshi, Sania & Aziz, Shaheen, 2020. "Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    7. Yusuf, Abdullahi & Qureshi, Sania & Feroz Shah, Syed, 2020. "Mathematical analysis for an autonomous financial dynamical system via classical and modern fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).

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