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Effects of stochastic perturbation and vaccinated age on a vector-borne epidemic model with saturation incidence rate

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  • Ran, Xue
  • Hu, Lin
  • Nie, Lin-Fei
  • Teng, Zhidong

Abstract

For reasons that the universality of stochastic perturbation and heterogeneity in the spread of vector-borne epidemic diseases, we formulate a stochastic vector-borne epidemic model with age-structure to discuss the effects of these factors. By constructing appropriate Lyapunov functions, the existence and uniqueness of global positive solutions of this model are derived. Further, we obtained some sufficient conditions for the extinction of the disease. In addition, the existence of a unique stationary distribution is studied which leads to the persistence of disease. Some numerical simulations are carried to explain our theoretical results. This implicates that, under the effects of these factors, the intensity and timing of outbreaks of the disease are unpredictable.

Suggested Citation

  • Ran, Xue & Hu, Lin & Nie, Lin-Fei & Teng, Zhidong, 2021. "Effects of stochastic perturbation and vaccinated age on a vector-borne epidemic model with saturation incidence rate," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    • Handle: RePEc:eee:apmaco:v:394:y:2021:i:c:s0096300320307517
    DOI: 10.1016/j.amc.2020.125798
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    References listed on IDEAS

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    1. Cai, Liming & Guo, Shumin & Li, XueZhi & Ghosh, Mini, 2009. "Global dynamics of a dengue epidemic mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2297-2304.
    2. Liu, Qun & Jiang, Daqing, 2019. "Dynamical behavior of a stochastic multigroup SIR epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    3. Wang, Lei & Teng, Zhidong & Ji, Chunyan & Feng, Xiaomei & Wang, Kai, 2019. "Dynamical behaviors of a stochastic malaria model: A case study for Yunnan, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 435-454.
    4. 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.
    5. 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.
    6. Li, Yingke & Teng, Zhidong & Hu, Cheng & Ge, Qing, 2017. "Global stability of an epidemic model with age-dependent vaccination, latent and relapse," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 195-207.
    7. Nudee, K. & Chinviriyasit, S. & Chinviriyasit, W., 2019. "The effect of backward bifurcation in controlling measles transmission by vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 400-412.
    8. 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.
    9. Srivastav, Akhil Kumar & Ghosh, Mini, 2019. "Assessing the impact of treatment on the dynamics of dengue fever: A case study of India," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
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