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Analysis of a deterministic and a stochastic epidemic model with two distinct epidemics hypothesis

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  • Boukanjime, Brahim
  • El Fatini, Mohamed
  • Laaribi, Aziz
  • Taki, Regragui

Abstract

In this paper, we discuss an epidemic model with double hypothesis combined two different transmission mechanisms. First, we prove the local asymptotic stability of the equilibrium solutions of deterministic system. Moreover we establish the global stability for the free equilibrium. Second, we show for stochastic system the extinction and persistence in mean of the disease, under some conditions on parameters of the model. Finally, numerical simulations are used to confirm our analytical results.

Suggested Citation

  • Boukanjime, Brahim & El Fatini, Mohamed & Laaribi, Aziz & Taki, Regragui, 2019. "Analysis of a deterministic and a stochastic epidemic model with two distinct epidemics hypothesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    • Handle: RePEc:eee:phsmap:v:534:y:2019:i:c:s0378437119313421
    DOI: 10.1016/j.physa.2019.122321
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    References listed on IDEAS

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    1. 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.
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    5. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 767-777.
    6. El Fatini, Mohamed & Lahrouz, Aadil & Pettersson, Roger & Settati, Adel & Taki, Regragui, 2018. "Stochastic stability and instability of an epidemic model with relapse," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 326-341.
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    Cited by:

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    2. Selvan, T. Tamil & Kumar, M., 2024. "Stationary distribution of a double epidemic stochastic model driven by saturated incidence rates," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    3. Boukanjime, Brahim & Caraballo, Tomás & El Fatini, Mohamed & El Khalifi, Mohamed, 2020. "Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    5. Selvan, T. Tamil & Kumar, M., 2023. "Dynamics of a deterministic and a stochastic epidemic model combined with two distinct transmission mechanisms and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).

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