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Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence

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  • Wang, Lianwen
  • Liu, Zhijun
  • Zhang, Xingan

Abstract

An SVEIR epidemic model with imperfect vaccination and nonlinear incidence, and a general latent distribution is formulated. By constructing Lyapunov functionals, it is shown that the disease will die out if the vaccination reproduction number Rvac≤1 and the disease becomes endemic if Rvac>1. Furthermore, vaccination effects are analyzed. Two special forms the probability of remaining in latent class are discussed. When the probability is negatively exponentially distributed, we present an efficient approach of proving global stability of the endemic equilibrium of the SVEIR system of ordinary differential equations (ODEs), which may improve some known approaches. When the probability is a step-function, the delay differential equation (DDE) system derived is used to study the impacts of vaccination and saturated incidence on the mumps transmission.

Suggested Citation

  • Wang, Lianwen & Liu, Zhijun & Zhang, Xingan, 2016. "Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 47-65.
    • Handle: RePEc:eee:apmaco:v:284:y:2016:i:c:p:47-65
    DOI: 10.1016/j.amc.2016.02.058
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    References listed on IDEAS

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    1. Sylvain Gandon & Margaret J. Mackinnon & Sean Nee & Andrew F. Read, 2001. "Imperfect vaccines and the evolution of pathogen virulence," Nature, Nature, vol. 414(6865), pages 751-756, December.
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    Cited by:

    1. Raul Nistal & Manuel De la Sen & Santiago Alonso-Quesada & Asier Ibeas, 2018. "On a New Discrete SEIADR Model with Mixed Controls: Study of Its Properties," Mathematics, MDPI, vol. 7(1), pages 1-19, December.
    2. Lu, Ruoxin & Wei, Fengying, 2019. "Persistence and extinction for an age-structured stochastic SVIR epidemic model with generalized nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 572-587.
    3. Li, Xiao-Ping & Din, Anwarud & Zeb, Anwar & Kumar, Sunil & Saeed, Tareq, 2022. "The impact of Lévy noise on a stochastic and fractal-fractional Atangana–Baleanu order hepatitis B model under real statistical data," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. Gao, Qingwu & Zhuang, Jun, 2020. "Stability analysis and control strategies for worm attack in mobile networks via a VEIQS propagation model," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    5. Sharma, Natasha & Gupta, Arvind Kumar, 2017. "Impact of time delay on the dynamics of SEIR epidemic model using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 114-125.
    6. Wang, Lianwen & Liu, Zhijun & Guo, Caihong & Li, Yong & Zhang, Xinan, 2021. "New global dynamical results and application of several SVEIS epidemic models with temporary immunity," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    7. Xin Liu & Zhou-Dao Lu & Ling-Zhi Li, 2018. "The Use of Bolted Side Plates for Shear Strengthening of RC Beams: A Review," Sustainability, MDPI, vol. 10(12), pages 1-15, December.
    8. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Stationary distribution of a stochastic delayed SVEIR epidemic model with vaccination and saturation incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 849-863.
    9. Khajji, Bouchaib & Kouidere, Abdelfatah & Elhia, Mohamed & Balatif, Omar & Rachik, Mostafa, 2021. "Fractional optimal control problem for an age-structured model of COVID-19 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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