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Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control

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  • Gao, Shujing
  • Zhong, Deming
  • Zhang, Yan

Abstract

In this paper, we establish two new stochastic switched epidemic models with continuous and impulsive control. The stochastic perturbations are considered for the natural death rate in each equation of the models. Firstly, a stochastic switched SILI model with continuous control schemes is investigated. By using Lyapunov–Razumikhin method, the sufficient conditions for extinction in mean are established. Our result shows that the disease could be die out theoretically if threshold value R is less than one, regardless of whether the disease-free solutions of the corresponding subsystems are stable or unstable. Then, a stochastic switched SILI model with continuous control schemes and pulse vaccination is studied. The threshold value R is derived. The global attractivity of the model is also obtained. At last, numerical simulations are carried out to support our results.

Suggested Citation

  • Gao, Shujing & Zhong, Deming & Zhang, Yan, 2018. "Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 162-171.
    • Handle: RePEc:eee:phsmap:v:495:y:2018:i:c:p:162-171
    DOI: 10.1016/j.physa.2017.12.050
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    References listed on IDEAS

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    1. Zhao, Yu & Yuan, Sanling, 2017. "Optimal harvesting policy of a stochastic two-species competitive model with Lévy noise in a polluted environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 20-33.
    2. Rifhat, Ramziya & Wang, Lei & Teng, Zhidong, 2017. "Dynamics for a class of stochastic SIS epidemic models with nonlinear incidence and periodic coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 176-190.
    3. Gao, Shujing & Liu, Yujiang & Nieto, Juan J. & Andrade, Helena, 2011. "Seasonality and mixed vaccination strategy in an epidemic model with vertical transmission," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1855-1868.
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    Cited by:

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    4. Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.

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