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Stationary distribution and extinction of the DS-I-A model disease with periodic parameter function and Markovian switching

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  • Liu, Songnan
  • Xu, Xiaojie
  • Jiang, Daqing
  • Hayat, Tasawar
  • Ahmad, Bashir

Abstract

This paper introduces the DS-I-A model with periodic parameter function and Markovian switching. First, we will prove that the solution of the system is positive and global. Furthermore, we draw a conclusion that there exists nontrivial positive periodic solution for the stochastic system and we establish sufficient conditions for extinction of system. Moreover, we construct stochastic Lyapunov functions with regime switching to obtain the existence of ergodic stationary distribution of the solution to DS-I-A model perturbed by white and telephone noises and we also establish sufficient conditions for extinction of system with regime switching. Finally, we test our theory conclusion by simulations.

Suggested Citation

  • Liu, Songnan & Xu, Xiaojie & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Stationary distribution and extinction of the DS-I-A model disease with periodic parameter function and Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 66-84.
    • Handle: RePEc:eee:apmaco:v:311:y:2017:i:c:p:66-84
    DOI: 10.1016/j.amc.2017.04.029
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    References listed on IDEAS

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    1. Lahrouz, Aadil & Omari, Lahcen, 2013. "Extinction and stationary distribution of a stochastic SIRS epidemic model with non-linear incidence," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 960-968.
    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.
    3. De la Sen, M. & Alonso-Quesada, S. & Ibeas, A., 2015. "On the stability of an SEIR epidemic model with distributed time-delay and a general class of feedback vaccination rules," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 953-976.
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    Cited by:

    1. Lin Hu & Lin-Fei Nie, 2022. "Dynamics of a Stochastic HIV Infection Model with Logistic Growth and CTLs Immune Response under Regime Switching," Mathematics, MDPI, vol. 10(19), pages 1-20, September.

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