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Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses

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  • Rajasekar, S.P.
  • Pitchaimani, M.

Abstract

A stochastically perturbed SIRS epidemic model with two viruses is formulated to investigate the effect of intensities of white noise on each population. We prove that the stochastic model has a non-negative solution that belongs to a positively invariant set. By applying a novel combination of suitable Lyapunov functions, we obtain that the asymptotic behaviour of the stochastic model holds a disease-free equilibrium if R0≤1 and investigate pth-moment exponential stability. Then we derive the sufficient conditions for the solution of the stochastic model that fluctuates around the endemic equilibrium if R0>1. Furthermore, the suitable conditions for the extinction and persistence of the diseases are established due to intensities of white noise in large. Finally, the theoretical results are illustrated by numerical investigations.

Suggested Citation

  • Rajasekar, S.P. & Pitchaimani, M., 2019. "Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 207-221.
    • Handle: RePEc:eee:chsofr:v:118:y:2019:i:c:p:207-221
    DOI: 10.1016/j.chaos.2018.11.023
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    References listed on IDEAS

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    Cited by:

    1. Omame, Andrew & Abbas, Mujahid & Din, Anwarud, 2023. "Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of SARS-CoV-2," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 302-336.
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    3. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2019. "Dynamic threshold probe of stochastic SIR model with saturated incidence rate and saturated treatment function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    4. Rajasekar, S.P. & Pitchaimani, M., 2020. "Ergodic stationary distribution and extinction of a stochastic SIRS epidemic model with logistic growth and nonlinear incidence," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    5. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    6. Xuan Leng & Asad Khan & Anwarud Din, 2023. "Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference," Mathematics, MDPI, vol. 11(8), pages 1-18, April.

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