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Stability analysis and system properties of Nipah virus transmission: A fractional calculus case study

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  • Baleanu, Dumitru
  • Shekari, Parisa
  • Torkzadeh, Leila
  • Ranjbar, Hassan
  • Jajarmi, Amin
  • Nouri, Kazem

Abstract

In this paper, we establish a Caputo-type fractional model to study the Nipah virus transmission dynamics. The model describes the impact of unsafe contact with an infectious corpse as a possible way to transmit this virus. The corresponding area to the system properties, including the positivity and boundedness of the solution, is explored by using the generalized fractional mean value theorem. Also, we investigate sufficient conditions for the local and global stability of the disease-free and the endemic steady-states based on the basic reproduction number R0. To show these important stability features, we employ fractional Routh–Hurwitz criterion and LaSalle’s invariability principle. For the implementation of this epidemic model, we also use the Adams–Bashforth–Moulton numerical method in a fractional sense. Finally, in addition to compare the fractional and classical results, as one of the main goals of this research, we demonstrate the usefulness of minimal unsafe touch with the infectious corpse. Simulation and comparative results verify the theoretical discussions.

Suggested Citation

  • Baleanu, Dumitru & Shekari, Parisa & Torkzadeh, Leila & Ranjbar, Hassan & Jajarmi, Amin & Nouri, Kazem, 2023. "Stability analysis and system properties of Nipah virus transmission: A fractional calculus case study," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922011699
    DOI: 10.1016/j.chaos.2022.112990
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    References listed on IDEAS

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    1. Agarwal, Praveen & Singh, Ram & Rehman, Attiq ul, 2021. "Numerical solution of hybrid mathematical model of dengue transmission with relapse and memory via Adam–Bashforth–Moulton predictor-corrector scheme," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Assefa Denekew Zewdie & Sunita Gakkhar, 2020. "A Mathematical Model for Nipah Virus Infection," Journal of Applied Mathematics, Hindawi, vol. 2020, pages 1-10, September.
    3. Majee, Suvankar & Jana, Soovoojeet & Das, Dhiraj Kumar & Kar, T.K., 2022. "Global dynamics of a fractional-order HFMD model incorporating optimal treatment and stochastic stability," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. Dokuyucu, Mustafa Ali & Dutta, Hemen, 2020. "A fractional order model for Ebola Virus with the new Caputo fractional derivative without singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Chávez, Joseph Páez & Wijaya, Karunia Putra & Pinto, Carla M.A. & Burgos-Simón, Clara, 2022. "A model for type I diabetes in an HIV-infected patient under highly active antiretroviral therapy," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
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    Cited by:

    1. Yan Qiao & Tao Lu, 2024. "Solvability of a Class of Fractional Advection–Dispersion Coupled Systems," Mathematics, MDPI, vol. 12(18), pages 1-18, September.
    2. Safoura Rezaei Aderyani & Reza Saadati & Donal O’Regan & Fehaid Salem Alshammari, 2023. "Fuzzy Approximate Solutions of Matrix-Valued Fractional Differential Equations by Fuzzy Control Functions," Mathematics, MDPI, vol. 11(6), pages 1-16, March.
    3. Azhar Iqbal Kashif Butt & Saira Batool & Muhammad Imran & Muneerah Al Nuwairan, 2023. "Design and Analysis of a New COVID-19 Model with Comparative Study of Control Strategies," Mathematics, MDPI, vol. 11(9), pages 1-29, April.
    4. Mukhtar, Roshana & Chang, Chuan-Yu & Raja, Muhammad Asif Zahoor & Chaudhary, Naveed Ishtiaq & Shu, Chi-Min, 2024. "Novel nonlinear fractional order Parkinson's disease model for brain electrical activity rhythms: Intelligent adaptive Bayesian networks," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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