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Modeling of measles epidemic with optimized fractional order under Caputo differential operator

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  • Qureshi, Sania
  • Jan, Rashid

Abstract

Memory is an important characteristic of an epidemic. One of such memory dependent and highly contagious viral diseases is measles that is also responsible for more than 140,000 deaths in 2018 in various regions of Asia and Africa. In order to better understand the transmission dynamics of measles, we have developed a new epidemiological model while considering both integer and fractional order operators and presented comparison. The Caputo fractional model has a unique solution with the positively invariant region. On the basis of basic reproduction number R0, stability analysis is discussed and sensitivity of parameters is investigated using PRCC global technique. Not only parameters but fractional order χ is also optimized via nonlinear least-squares approach with availability of statistical data obtained from WHO. Various simulations in terms of time series plots, 3D meshes and contours are carried out to observe effects of parameters on dynamics of the epidemic wherein it is said to be persistent for χ→0 demonstrating the role being played by Caputo fractional derivative towards measles dynamics.

Suggested Citation

  • Qureshi, Sania & Jan, Rashid, 2021. "Modeling of measles epidemic with optimized fractional order under Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001181
    DOI: 10.1016/j.chaos.2021.110766
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    References listed on IDEAS

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    1. Pang, Liuyong & Ruan, Shigui & Liu, Sanhong & Zhao, Zhong & Zhang, Xinan, 2015. "Transmission dynamics and optimal control of measles epidemics," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 131-147.
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    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. 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).
    5. Emmanuel Njeuhmeli & Melissa Schnure & Andrea Vazzano & Elizabeth Gold & Peter Stegman & Katharine Kripke & Michel Tchuenche & Lori Bollinger & Steven Forsythe & Catherine Hankins, 2019. "Using mathematical modeling to inform health policy: A case study from voluntary medical male circumcision scale-up in eastern and southern Africa and proposed framework for success," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-15, March.
    6. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    7. 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).
    8. Emile Franc Doungmo Goufo & Suares Clovis Oukouomi Noutchie & Stella Mugisha, 2014. "A Fractional SEIR Epidemic Model for Spatial and Temporal Spread of Measles in Metapopulations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, June.
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    Cited by:

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    2. Alfifi, H.Y., 2022. "Stability analysis for Schnakenberg reaction-diffusion model with gene expression time delay," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Shah Hussain & Elissa Nadia Madi & Naveed Iqbal & Thongchai Botmart & Yeliz Karaca & Wael W. Mohammed, 2021. "Fractional Dynamics of Vector-Borne Infection with Sexual Transmission Rate and Vaccination," Mathematics, MDPI, vol. 9(23), pages 1-22, December.
    4. Shah, Kamal & Arfan, Muhammad & Ullah, Aman & Al-Mdallal, Qasem & Ansari, Khursheed J. & Abdeljawad, Thabet, 2022. "Computational study on the dynamics of fractional order differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. El-Mesady, A. & Elsonbaty, Amr & Adel, Waleed, 2022. "On nonlinear dynamics of a fractional order monkeypox virus model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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