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Threshold behaviour of a stochastic epidemic model with two-dimensional noises

Author

Listed:
  • El Fatini, M.
  • Taki, R.
  • Tridane, A.

Abstract

The aim of this work is to study a new stochastic SIR epidemic model that includes two types of white noises. These noises perturb two important parameters in the disease dynamic: the disease transmission rate and the recovery rate. By means of the Lyapunov functions, we prove the global existence and positivity of the solution. We also investigate the conditions of the extinction and the persistence of the disease and use a suitable Lyapunov function to study the stability of the model. Numerical simulations of our result are also presented.

Suggested Citation

  • El Fatini, M. & Taki, R. & Tridane, A., 2019. "Threshold behaviour of a stochastic epidemic model with two-dimensional noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 776-786.
    • Handle: RePEc:eee:phsmap:v:524:y:2019:i:c:p:776-786
    DOI: 10.1016/j.physa.2019.04.224
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    References listed on IDEAS

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    3. 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.
    4. Tornatore, Elisabetta & Maria Buccellato, Stefania & Vetro, Pasquale, 2005. "Stability of a stochastic SIR system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 111-126.
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