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A stochastic SIRS epidemic model with a general awareness-induced incidence

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  • Berrhazi, Badreddine
  • El Fatini, Mohamed
  • Lahrouz, Aadil
  • Settati, Adel
  • Taki, Regragui

Abstract

In this work we investigate the existence of a unique global positive solution for a stochastic SIRS epidemic model with a general awareness-induced incidence. We also study the dynamic properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we establish sufficient conditions for the existence of an ergodic stationary distribution to the model. Numerical simulations are presented to confirm the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:968-980
    DOI: 10.1016/j.physa.2018.08.150
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    References listed on IDEAS

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    1. Lin, Yuguo & Jiang, Daqing & Wang, Shuai, 2014. "Stationary distribution of a stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 187-197.
    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.
    3. 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.
    4. Liu, Wenbin & Zheng, Qiben, 2015. "A stochastic SIS epidemic model incorporating media coverage in a two patch setting," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 160-168.
    5. 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:

    1. Zhou, Baoquan & Han, Bingtao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. El Attouga, Sanae & Bouggar, Driss & El Fatini, Mohamed & Hilbert, Astrid & Pettersson, Roger, 2023. "Lévy noise with infinite activity and the impact on the dynamic of an SIRS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    3. El Fatini, Mohamed & Sekkak, Idriss & Laaribi, Aziz, 2019. "A threshold of a delayed stochastic epidemic model with Crowly–Martin functional response and vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 151-160.
    4. 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).
    5. 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).

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