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Transmission dynamics of Zika virus with spatial structure—A case study in Rio de Janeiro, Brazil

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  • Cai, Yongli
  • Ding, Zuqin
  • Yang, Bin
  • Peng, Zhihang
  • Wang, Weiming

Abstract

In this paper, we investigate the effect of the spatial heterogeneity on the extinction and persistence of the Zika virus (ZIKV) further. We define the basic reproduction number R0 and prove that R0 can be used to govern the threshold dynamics of the ZIKV: if R0<1, the unique disease-free equilibrium is globally asymptotic stable and the ZIKV will die out, while if R0>1, there is at least one endemic equilibrium and the ZIKV will persist uniformly. Via numerical simulations, we show the evolution of the spatial distribution of infected people and find that the final size of the infected people is 25,717, which agrees nearly with the real weekly reported case data 25,400 from November 1, 2015 to April 10, 2016 in Rio de Janeiro, Brazil.

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  • Cai, Yongli & Ding, Zuqin & Yang, Bin & Peng, Zhihang & Wang, Weiming, 2019. "Transmission dynamics of Zika virus with spatial structure—A case study in Rio de Janeiro, Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 729-740.
    • Handle: RePEc:eee:phsmap:v:514:y:2019:i:c:p:729-740
    DOI: 10.1016/j.physa.2018.09.100
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    References listed on IDEAS

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    1. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    2. Wang, Weiming & Cai, Yongli & Ding, Zuqin & Gui, Zhanji, 2018. "A stochastic differential equation SIS epidemic model incorporating Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 921-936.
    3. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
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    Cited by:

    1. Zhang, Baoxiang & Cai, Yongli & Wang, Bingxian & Wang, Weiming, 2019. "Pattern formation in a reaction–diffusion parasite–host model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 732-740.
    2. Luo, Yantao & Zhang, Long & Zheng, Tingting & Teng, Zhidong, 2019. "Analysis of a diffusive virus infection model with humoral immunity, cell-to-cell transmission and nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Lívia Madeira Triaca & Felipe Garcia Ribeiro & César Augusto Oviedo Tejada, 2021. "Mosquitoes, birth rates and regional spillovers: Evidence from the Zika epidemic in Brazil," Papers in Regional Science, Wiley Blackwell, vol. 100(3), pages 795-813, June.
    4. Zhang, Chao & Gao, Jianguo & Sun, Hongquan & Wang, Jinliang, 2019. "Dynamics of a reaction–diffusion SVIR model in a spatial heterogeneous environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C), pages 1-1.

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