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Dynamics analysis of a Zika–dengue co-infection model with dengue vaccine and antibody-dependent enhancement

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  • Wang, Liping
  • Zhao, Hongyong

Abstract

Mounting clinical and experimental evidence indicates that antibodies against dengue can enhance Zika infection through the antibody-dependent enhancement (ADE) mechanism. ADE is an alarming evolutionary development that makes it difficult to develop a vaccination campaign against dengue. To better understand the effect of dengue vaccine and ADE on a Zika and dengue outbreak, we formulate a Zika–dengue co-infection model that describes the joint dynamics of Zika and dengue. We derive the basic and invasion reproduction numbers, which are threshold values to identify the existence and stability of a disease-free state and two boundary equilibrium points, where only one strain (Zika or dengue) is present, and to identify the persistence of disease. Our analysis and numerical simulations suggest that although vaccination against dengue has a positive effect on the control of dengue, it has a negative effect on the control of Zika, and the increasing level of ADE induces a large number of accumulated Zika cases. Later, in this paper, criteria of vaccination against dengue strategies are established for disease eradication. Finally, the model is applied to simulate the accumulated cases of Zika and dengue in Brazil from February 19, 2016 to April 14, 2018. Based on the parameters estimated, we obtain that in Brazil the dengue epidemic is endemic whereas the Zika epidemic will eventually disappear.

Suggested Citation

  • Wang, Liping & Zhao, Hongyong, 2019. "Dynamics analysis of a Zika–dengue co-infection model with dengue vaccine and antibody-dependent enhancement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 248-273.
    • Handle: RePEc:eee:phsmap:v:522:y:2019:i:c:p:248-273
    DOI: 10.1016/j.physa.2019.01.099
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    References listed on IDEAS

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    1. Saba, H. & Miranda, J.G.V. & Moret, M.A., 2014. "Self-organized critical phenomenon as a q-exponential decay — Avalanche epidemiology of dengue," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 205-211.
    2. Pereira, F.M.M. & Schimit, P.H.T., 2018. "Dengue fever spreading based on probabilistic cellular automata with two lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 75-87.
    3. Bicout, D.J. & Chalvet-Monfray, K. & Sabatier, P., 2002. "Infection persistence time of Aedes breeding habitats," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(3), pages 597-603.
    4. Barmak, D.H. & Dorso, C.O. & Otero, M., 2016. "Modelling dengue epidemic spreading with human mobility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 129-140.
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    Cited by:

    1. 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).
    2. Abidemi, Afeez & Owolabi, Kolade M. & Pindza, Edson, 2022. "Modelling the transmission dynamics of Lassa fever with nonlinear incidence rate and vertical transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

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