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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. 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.
    2. 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.
    3. 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.
    4. Chang, Zhengbo & Meng, Xinzhu & Lu, Xiao, 2017. "Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 103-116.
    5. Haokun Qi & Lidan Liu & Xinzhu Meng, 2017. "Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis," Complexity, Hindawi, vol. 2017, pages 1-14, November.
    6. Berrhazi, Badreddine & El Fatini, Mohamed & Lahrouz, Aadil & Settati, Adel & Taki, Regragui, 2018. "A stochastic SIRS epidemic model with a general awareness-induced incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 968-980.
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    Cited by:

    1. 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).
    2. Laaribi, Aziz & Boukanjime, Brahim & El Khalifi, Mohamed & Bouggar, Driss & El Fatini, Mohamed, 2023. "A generalized stochastic SIRS epidemic model incorporating mean-reverting Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(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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