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On a Stochastic SEIS Model with Treatment Rate of Latent Population

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  • Shujing Gao
  • Yanfei Dai
  • Yan Zhang
  • Yujiang Liu

Abstract

The asymptotic dynamics of a stochastic SEIS epidemic model with treatment rate of latent population is investigated. First, we show that the system provides a unique positive global solution starting from the positive initial value. Then, the long‐term asymptotic behavior of the model is studied: if R0, which is called the basic reproduction number of the corresponding deterministic model, is not more than unity, the solution of the model is oscillating around the disease‐free equilibrium of the corresponding deterministic system, whereas if R0 is larger than unity, we show how the solution spirals around the endemic equilibrium of deterministic system under certain parametric restrictions. Finally, numerical simulations are carried out to support our theoretical findings.

Suggested Citation

  • Shujing Gao & Yanfei Dai & Yan Zhang & Yujiang Liu, 2014. "On a Stochastic SEIS Model with Treatment Rate of Latent Population," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:894842
    DOI: 10.1155/2014/894842
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    References listed on IDEAS

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    1. Jin, Yu & Wang, Wendi & Xiao, Shiwu, 2007. "An SIRS model with a nonlinear incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1482-1497.
    2. Jinghai Wang, 2012. "Analysis of an SEIS Epidemic Model with a Changing Delitescence," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, August.
    3. Ji, Chunyan & Jiang, Daqing & Shi, Ningzhong, 2011. "Multigroup SIR epidemic model with stochastic perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(10), pages 1747-1762.
    4. Qixing Han & Daqing Jiang & Chengjun Yuan, 2013. "Extinction and Ergodic Property of Stochastic SIS Epidemic Model with Nonlinear Incidence Rate," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Jinghai Wang, 2012. "Analysis of an SEIS Epidemic Model with a Changing Delitescence," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Qixing Han & Daqing Jiang & Chengjun Yuan, 2013. "Extinction and Ergodic Property of Stochastic SIS Epidemic Model with Nonlinear Incidence Rate," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, December.
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