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Fractional Dynamics of Vector-Borne Infection with Sexual Transmission Rate and Vaccination

Author

Listed:
  • Shah Hussain

    (Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin (UniSZA), Besut Campus, Terengganu 22200, Malaysia)

  • Elissa Nadia Madi

    (Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin (UniSZA), Besut Campus, Terengganu 22200, Malaysia)

  • Naveed Iqbal

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 81481, Saudi Arabia)

  • Thongchai Botmart

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Yeliz Karaca

    (UMass Medical School, University of Massachusetts, 55 Lake Avenue North, Worcester, MA 01655, USA)

  • Wael W. Mohammed

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 81481, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

New fractional operators have the aim of attracting nonlocal problems that display fractal behaviour; and thus fractional derivatives have applications in long-term relation description along with micro-scaled and macro-scaled phenomena. Formulated by fractional operators, the formulation of a dynamical system is used in applications for the description of systems with long-range interactions. Vector-borne illnesses are one of the world’s most serious public health issues with a large economic impact on the nations that are impacted. Population increase, urbanization, globalization, and a lack of public health infrastructure have all had a role in the introduction and reemergence of vector-borne illnesses during the last four decades. The control of these infections are important to lessen the economic burden of vector-borne diseases in infected regions. In this research work, we formulate the transmission process of Zika virus with the impact of sexual incidence rate and vaccination in terms of mathematics. We presented the fundamental theory of fractional operators Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) for the analysis of the proposed system. We examine our system of Zika infection and determined the endemic indicator through a next-generation matrix technique. The uniqueness and existence of the solution has been investigated through fixed point theory. Accordingly, a numerical method has been introduced to investigate the dynamical nature of the system and make a comparison of the outcomes of the operators. The impact of different input factors has been conceptualized through dynamical behaviour of the system. We observed that lowering the index of memory, the fractional system provides accurate results about the recommended Zika dynamics and dramatically reduces infected people. It has been proved that high efficacy of a vaccine can lower the level of infection. Moreover, the impact of other parameters on the system of Zika virus infection are highlighted through numerical results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3118-:d:694469
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    References listed on IDEAS

    as
    1. Qureshi, Sania & Jan, Rashid, 2021. "Modeling of measles epidemic with optimized fractional order under Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Ebenezer Bonyah & Muhammad Altaf Khan & K O Okosun & Saeed Islam, 2017. "A theoretical model for Zika virus transmission," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-26, October.
    3. Jan, Rashid & Khan, Muhammad Altaf & Kumam, Poom & Thounthong, Phatiphat, 2019. "Modeling the transmission of dengue infection through fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 189-216.
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    Cited by:

    1. Yasmin, Humaira, 2022. "Effect of vaccination on non-integer dynamics of pneumococcal pneumonia infection," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Tariq Q. S. Abdullah & Gang Huang & Wadhah Al-Sadi & Yasser Aboelmagd & Wael Mobarak, 2024. "Fractional Dynamics of Cassava Mosaic Disease Model with Recovery Rate Using New Proposed Numerical Scheme," Mathematics, MDPI, vol. 12(15), pages 1-24, July.

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