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Dynamics of a stochastic tuberculosis model with antibiotic resistance

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  • Liu, Qun
  • Jiang, Daqing
  • Hayat, Tasawar
  • Alsaedi, Ahmed

Abstract

In this paper, we study a stochastic tuberculosis model with antibiotic resistance. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Moreover, we obtain sufficient conditions for extinction of the disease. The existence of a stationary distribution implies stochastic weak stability.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Dynamics of a stochastic tuberculosis model with antibiotic resistance," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 223-230.
    • Handle: RePEc:eee:chsofr:v:109:y:2018:i:c:p:223-230
    DOI: 10.1016/j.chaos.2018.02.033
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    References listed on IDEAS

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    1. Sharma, Natasha & Gupta, Arvind Kumar, 2017. "Impact of time delay on the dynamics of SEIR epidemic model using cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 114-125.
    2. 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.
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    Cited by:

    1. Das, Dhiraj Kumar & Kar, T.K., 2021. "Global dynamics of a tuberculosis model with sensitivity of the smear microscopy," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Fathalla A. Rihan & Chinnathambi Rajivganthi, 2021. "Dynamics of Tumor-Immune System with Random Noise," Mathematics, MDPI, vol. 9(21), pages 1-14, October.
    3. Borah, Manashita & Das, Debanita & Gayan, Antara & Fenton, Flavio & Cherry, Elizabeth, 2021. "Control and anticontrol of chaos in fractional-order models of Diabetes, HIV, Dengue, Migraine, Parkinson's and Ebola virus diseases," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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