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Dynamics of a deterministic and a stochastic epidemic model combined with two distinct transmission mechanisms and saturated incidence rate

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  • Selvan, T. Tamil
  • Kumar, M.

Abstract

The study of dynamics of epidemics, especially, double epidemics, has got paramount importance in the present days, since various health risks, an individual is exposed to due to the increasing global warming are unavoidable and/or due to limited medical resources available to handle suddenly developed disease. In view of this, we consider a study of an epidemic model with a double hypothesis, namely, SIR and SIRS mechanisms. First, we prove the local asymptotic stability of equilibrium points followed by the global stability of the disease for equilibrium established through the Lyapunov function. Next, we show the existence, extinction and persistence results of the stochastic system. Finally, some numerical examples are presented to support the theoretical results established.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:619:y:2023:i:c:s0378437123002960
    DOI: 10.1016/j.physa.2023.128741
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    4. Tabassum, Muhammad Farhan & Saeed, Muhammad & Akgül, Ali & Farman, Muhammad & Chaudhry, Nazir Ahmad, 2020. "Treatment of HIV/AIDS epidemic model with vertical transmission by using evolutionary Padé-approximation," Chaos, Solitons & Fractals, Elsevier, vol. 134(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).
    6. Li, Guihua & Zhen, Jin, 2005. "Global stability of an SEI epidemic model with general contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 997-1004.
    7. De la Sen, M. & Alonso-Quesada, S. & Ibeas, A., 2015. "On the stability of an SEIR epidemic model with distributed time-delay and a general class of feedback vaccination rules," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 953-976.
    8. 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.
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    1. 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).

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