IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i23p3118-d694469.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/23/3118/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/23/3118/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Qureshi, Sania & Jan, Rashid, 2021. "Modeling of measles epidemic with optimized fractional order under Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kumar, Sunil & Chauhan, R.P. & Momani, Shaher & Hadid, Samir, 2021. "A study of fractional TB model due to mycobacterium tuberculosis bacteria," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    2. Ghosh, M. & Olaniyi, S. & Obabiyi, O.S., 2020. "Mathematical analysis of reinfection and relapse in malaria dynamics," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    3. Kolebaje, Olusola & Popoola, Oyebola & Khan, Muhammad Altaf & Oyewande, Oluwole, 2020. "An epidemiological approach to insurgent population modeling with the Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Malik, Hafiz Abid Mahmood & Abid, Faiza & Wahiddin, Mohamed Ridza & Waqas, Ahmad, 2021. "Modeling of internal and external factors affecting a complex dengue network," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Ali, Hegagi Mohamed & Ameen, Ismail Gad, 2021. "Optimal control strategies of a fractional order model for Zika virus infection involving various transmissions," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Alfifi, H.Y., 2022. "Stability analysis for Schnakenberg reaction-diffusion model with gene expression time delay," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    7. Attaullah, & Jan, Rashid & Yüzbaşı, Şuayip, 2021. "Dynamical behaviour of HIV Infection with the influence of variable source term through Galerkin method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. 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).
    9. 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).
    10. Khan, Muhammad Altaf & Islam, Saeed & Zaman, Gul, 2018. "Media coverage campaign in Hepatitis B transmission model," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 378-393.
    11. Woldegerima, Woldegebriel Assefa & Ouifki, Rachid & Banasiak, Jacek, 2021. "Mathematical analysis of the impact of transmission-blocking drugs on the population dynamics of malaria," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    12. Hasan, Bushra & Singh, Manmohan & Richards, David & Blicblau, Aaron, 2019. "Mathematical modelling of Zika virus as a mosquito-borne and sexually transmitted disease with diffusion effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 56-75.
    13. Addai, Emmanuel & Zhang, Lingling & Ackora-Prah, Joseph & Gordon, Joseph Frank & Asamoah, Joshua Kiddy K. & Essel, John Fiifi, 2022. "Fractal-fractional order dynamics and numerical simulations of a Zika epidemic model with insecticide-treated nets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    14. L., Diego F. Aranda & González-Parra, Gilberto & Benincasa, Tommaso, 2019. "Mathematical modeling and numerical simulations of Zika in Colombia considering mutation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 1-18.
    15. Yasmin, Humaira, 2022. "Effect of vaccination on non-integer dynamics of pneumococcal pneumonia infection," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    16. Meskaf, Adil & Khyar, Omar & Danane, Jaouad & Allali, Karam, 2020. "Global stability analysis of a two-strain epidemic model with non-monotone incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    17. Soukhovolsky, Vladislav & Kovalev, Anton & Pitt, Anne & Kessel, Boris, 2020. "A new modelling of the COVID 19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    18. Farman, Muhammad & Xu, Changjin & Shehzad, Aamir & Akgul, Ali, 2024. "Modeling and dynamics of measles via fractional differential operator of singular and non-singular kernels," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 461-488.
    19. Esteban Dodero-Rojas & Luiza G Ferreira & Vitor B P Leite & José N Onuchic & Vinícius G Contessoto, 2020. "Modeling Chikungunya control strategies and Mayaro potential outbreak in the city of Rio de Janeiro," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-13, January.
    20. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3118-:d:694469. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.