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Mathematical modeling and numerical simulations of Zika in Colombia considering mutation

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  • L., Diego F. Aranda
  • González-Parra, Gilberto
  • Benincasa, Tommaso

Abstract

In this paper, we analyze the Zika virus transmission dynamics on human and mosquito populations. Mosquitoes play a role of infectious agents and vector of the Zika virus (ZIKV). In this sense, we set out a mathematical model assuming constant size population for the evolution of the infected humans with ZIKV and analyze its qualitative dynamics. The epidemic threshold parameter R0 for the extinction of disease is computed. Numerical simulations of the model varying the numerical values of the parameters corroborate the theoretical results regarding R0. The values of the parameters related to the mathematical model of the Zika epidemic are estimated using real data from Zika prevalence in Colombia for year 2016. We find a R0=0.88 for this particular case which allows us to understand and explain some aspects of the Zika epidemic in Colombia. These results are valuable since they can be compared with Zika epidemics in other countries and from other years, and enrich the knowledge about the dynamics of the spread of Zika virus.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:163:y:2019:i:c:p:1-18
    DOI: 10.1016/j.matcom.2019.02.009
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    References listed on IDEAS

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    1. Laith Yakob & Archie C A Clements, 2013. "A Mathematical Model of Chikungunya Dynamics and Control: The Major Epidemic on Réunion Island," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-6, March.
    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. Khan, Muhammad Altaf & Khan, Rizwan & Khan, Yasir & Islam, Saeed, 2018. "A mathematical analysis of Pine Wilt disease with variable population size and optimal control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 205-217.
    4. Arenas, Abraham J. & González-Parra, Gilberto & Villanueva Micó, Rafael-J., 2010. "Modeling toxoplasmosis spread in cat populations under vaccination," Theoretical Population Biology, Elsevier, vol. 77(4), pages 227-237.
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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. 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).
    3. Abraham J. Arenas & Gilberto González-Parra & Jhon J. Naranjo & Myladis Cogollo & Nicolás De La Espriella, 2021. "Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay," Mathematics, MDPI, vol. 9(3), pages 1-21, January.

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