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A delayed diffusive influenza model with two-strain and two vaccinations

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  • Chen, Zhenwu
  • Xu, Zhiting

Abstract

This paper deals with the global stability of a delayed diffusive influenza model with two-strain and two vaccinations. First, we consider the well-posedness of solutions of the model and show that the model admits four constant equilibria: a disease-free equilibrium, two single-strain-infection equilibria, and a double-strain-infection equilibrium, which are determined by three threshold parameters R1,R2 and R3 (or R4). Second, constructing four suitable Lyapunov functionals and using the LaSalle’s invariant principle, we establish the global stability of these equilibria. Finally, we give several numerical simulations to illustrates the analytic results.

Suggested Citation

  • Chen, Zhenwu & Xu, Zhiting, 2019. "A delayed diffusive influenza model with two-strain and two vaccinations," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 439-453.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:439-453
    DOI: 10.1016/j.amc.2018.12.065
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    References listed on IDEAS

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    1. Bilgen Kaymakamzade & Evren Hincal, 2018. "Two-strain epidemic model with two vaccinations and two time delayed," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(1), pages 695-709, December.
    2. Baba, Isa Abdullahi & Kaymakamzade, Bilgen & Hincal, Evren, 2018. "Two-strain epidemic model with two vaccinations," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 342-348.
    3. Xu, Zhiting & Qu, Liangcheng & Huang, Yehui, 2016. "Global dynamics of a two-strain flu model with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 124(C), pages 44-59.
    4. Xu, Zhiting & Zhao, Yingying, 2015. "A diffusive dengue disease model with nonlocal delayed transmission," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 808-829.
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    Cited by:

    1. Fu, Minglei & Feng, Jun & Lande, Dmytro & Dmytrenko, Oleh & Manko, Dmytro & Prakapovich, Ryhor, 2021. "Dynamic model with super spreaders and lurker users for preferential information propagation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    2. Yufang Wang & Kuai Xu & Yun Kang & Haiyan Wang & Feng Wang & Adrian Avram, 2020. "Regional Influenza Prediction with Sampling Twitter Data and PDE Model," IJERPH, MDPI, vol. 17(3), pages 1-12, January.
    3. Farah, El Mehdi & Amine, Saida & Allali, Karam, 2021. "Dynamics of a time-delayed two-strain epidemic model with general incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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