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Extinction and periodic solutions for an impulsive SIR model with incidence rate stochastically perturbed

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  • Pan, Tao
  • Jiang, Daqing
  • Hayat, Tasawar
  • Alsaedi, Ahmed

Abstract

In this paper, we consider an impulsive SIR model with incidence rate stochastically perturbed. First, we prove the existence and uniqueness of the global positive solution by constructing the equivalent system without impulse. Second, we obtain a sufficient condition which determines epidemic to extinct. Then we demonstrate the existence and global attraction of the boundary periodic solution under the certain condition. Finally, we present a sufficient condition which allows the existence of a positive periodic solution.

Suggested Citation

  • Pan, Tao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Extinction and periodic solutions for an impulsive SIR model with incidence rate stochastically perturbed," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 385-397.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:385-397
    DOI: 10.1016/j.physa.2018.03.012
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    References listed on IDEAS

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    1. 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.
    2. 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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    Cited by:

    1. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Satoh, Daisuke & Uchida, Masato, 2021. "Riccati equation as topology-based model of computer worms and discrete SIR model with constant infectious period," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).

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