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Stability and extinction of SEIR epidemic models with generalized nonlinear incidence

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  • Wei, Fengying
  • Xue, Rui

Abstract

We investigate the global asymptotic stabilities of disease-free equilibrium and endemic equilibrium of the deterministic susceptible–exposed–infected–recovered epidemic model (short for SEIR model). The basic reproduction number R0, depends on constant contact rate β and natural death rate d and other parameters as well, indicates the critical value of stability, and completely determines the dynamical behavior of the deterministic model. After taking the perturbations of the environments into account, the corresponding stochastic SEIR model with generalized nonlinear incidence is discussed in existence and uniqueness, the extinction in the mean, and the existence of the unique stationary distribution as well. As a consequence, we carry out several numerical simulations to support the main theoretical results of this paper.

Suggested Citation

  • Wei, Fengying & Xue, Rui, 2020. "Stability and extinction of SEIR epidemic models with generalized nonlinear incidence," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 1-15.
    • Handle: RePEc:eee:matcom:v:170:y:2020:i:c:p:1-15
    DOI: 10.1016/j.matcom.2018.09.029
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    References listed on IDEAS

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    1. Li, Guihua & Jin, Zhen, 2005. "Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1177-1184.
    2. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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    Cited by:

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