IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0185540.html
   My bibliography  Save this article

A theoretical model for Zika virus transmission

Author

Listed:
  • Ebenezer Bonyah
  • Muhammad Altaf Khan
  • K O Okosun
  • Saeed Islam

Abstract

In this paper, we present and analyze an SEIR Zika epidemic model. Firstly, we investigate the model with constant controls. The steady states of the model is found to be locally and globally asymptotically stable. Thereafter, we incorporate time dependent controls into the model in order to investigate the optimal effects of bednets, treatments of infective and spray of insecticides on the disease spread. Furthermore, we used Pontryagin’s Maximum Principle to determine the necessary conditions for effective control of the disease. Also, the numerical results were presented.

Suggested Citation

  • 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.
    • Handle: RePEc:plo:pone00:0185540
    DOI: 10.1371/journal.pone.0185540
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0185540
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0185540&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0185540?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Xing, Yi & Song, Lipeng & Sun, Gui-Quan & Jin, Zhen & Zhang, Juan, 2017. "Assessing reappearance factors of H7N9 avian influenza in China," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 192-204.
    2. Hui Wan & Jing-an Cui, 2013. "Rich Dynamics of an Epidemic Model with Saturation Recovery," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, April.
    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. 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).
    2. 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.
    3. 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).
    4. 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.
    5. 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).
    6. 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).
    7. 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).
    8. 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.
    9. Soukhovolsky, Vladislav & Kovalev, Anton & Pitt, Anne & Kessel, Boris, 2020. "A new modelling of the COVID 19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    10. 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.
    11. 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.

    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. Chen, Dandan & Zheng, Muhua & Zhao, Ming & Zhang, Yu, 2018. "A dynamic vaccination strategy to suppress the recurrent epidemic outbreaks," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 108-114.
    2. Li, Qian & Xiao, Yanni, 2023. "Analysis of a hybrid SIR model combining the fixed-moments pulse interventions with susceptibles-triggered threshold policy," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    3. Suo, Qi & Guo, Jin-Li & Shen, Ai-Zhong, 2018. "Information spreading dynamics in hypernetworks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 475-487.
    4. Wu, Yong-Ping & Zhu, Chun-yangzi & Feng, Guo-Lin & Li, B. Larry, 2018. "Mathematical modeling of Fog-Haze evolution," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 1-4.
    5. Li, Li, 2017. "Transmission dynamics of Ebola virus disease with human mobility in Sierra Leone," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 575-579.
    6. Guo, Zun-Guang & Sun, Gui-Quan & Wang, Zhen & Jin, Zhen & Li, Li & Li, Can, 2020. "Spatial dynamics of an epidemic model with nonlocal infection," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    7. Bekiros, Stelios & Kouloumpou, Dimitra, 2020. "SBDiEM: A new mathematical model of infectious disease dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    8. M., Pitchaimani & M., Brasanna Devi, 2020. "Random effects in HIV infection model at Eclipse stage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    9. Yongxue Chen & Hui Zhang & Jingyu Wang & Cheng Li & Ning Yi & Yongxian Wen, 2022. "Analyzing an Epidemic of Human Infections with Two Strains of Zoonotic Virus," Mathematics, MDPI, vol. 10(7), pages 1-27, March.
    10. Gashirai, Tinashe B. & Musekwa-Hove, Senelani D. & Lolika, Paride O. & Mushayabasa, Steady, 2020. "Global stability and optimal control analysis of a foot-and-mouth disease model with vaccine failure and environmental transmission," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    11. Juping Zhang & Yun Li & Zhen Jin & Huaiping Zhu, 2019. "Dynamics Analysis of an Avian Influenza A (H7N9) Epidemic Model with Vaccination and Seasonality," Complexity, Hindawi, vol. 2019, pages 1-15, March.
    12. Li, Can & Guo, Zun-Guang & Zhang, Zhi-Yu, 2017. "Transmission dynamics of a brucellosis model: Basic reproduction number and global analysis," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 161-172.
    13. Sui, Xin & Li, Liang, 2018. "Guarantee network model and risk contagion," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 323-329.
    14. Baba, Isa Abdullahi & Hincal, Evren, 2018. "A model for influenza with vaccination and awareness," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 49-55.
    15. Feng, Guo-Lin & Yang, Jie & Zhi, Rong & Zhao, Jun-Hu & Gong, Zhi-Qiang & Zheng, Zhi-Hai & Xiong, Kai-Guo & Qiao, Shao-Bo & Yan, Ziheng & Wu, Yong-Ping & Sun, Gui-Quan, 2020. "Improved prediction model for flood-season rainfall based on a nonlinear dynamics-statistic combined method," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    16. Wen, Haijun & Hou, Shiwang & Liu, Zhaohua & Liu, Yongjiang, 2017. "An optimization algorithm for integrated remanufacturing production planning and scheduling system," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 69-76.
    17. Biswas, Santanu, 2017. "Mathematical modeling of Visceral Leishmaniasis and control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 546-556.
    18. Wang, Caiyun & Qi, Suying, 2018. "Spatial dynamics of a predator-prey system with cross diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 55-60.
    19. Mbabazi, Fulgensia Kamugisha & Mugisha, J.Y.T. & Kimathi, M., 2018. "Modeling the within-host co-infection of influenza A virus and pneumococcus," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 488-506.
    20. Wu, Zeyan & Li, Jianjuan & Li, Jing & Liu, Shuying & Zhou, Liuting & Luo, Yang, 2017. "Pattern formations of an epidemic model with Allee effect and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 599-606.

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0185540. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.