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A theoretical model for Zika virus transmission

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. 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).
    2. 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).
    3. 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).
    4. 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.
    5. 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).
    6. 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.
    7. Soukhovolsky, Vladislav & Kovalev, Anton & Pitt, Anne & Kessel, Boris, 2020. "A new modelling of the COVID 19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. 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.
    9. 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.
    10. 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.
    11. 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).

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