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Thermostated Susceptible-Infected-Susceptible epidemic model

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  • Alrebdi, H.I.
  • Steklain, Andre
  • Amorim, Edgard P.M.
  • Zotos, Euaggelos

Abstract

The evolution of epidemics based on the Susceptible-Infected-Susceptible (SIS) model relies on the density of infected individuals ρ. Recent results show that the mean density 〈ρ〉 and its variance σ2 can be regarded as canonical variables and obey Hamilton’s equations. Using the Hamiltonian formulation, we study the SIS system coupled to a Nosé thermal bath. We reinterpret classical parameters like temperature in an epidemiological context. In contrast to classical epidemiological models, the thermal bath modifies the dynamical behavior of the system by introducing fluctuations, such as those seen in some infectious waves. We study the stability and show that 〈ρ〉 tends to be half of the value predicted by the original SIS model.

Suggested Citation

  • Alrebdi, H.I. & Steklain, Andre & Amorim, Edgard P.M. & Zotos, Euaggelos, 2023. "Thermostated Susceptible-Infected-Susceptible epidemic model," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    • Handle: RePEc:eee:apmaco:v:441:y:2023:i:c:s009630032200769x
    DOI: 10.1016/j.amc.2022.127701
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    References listed on IDEAS

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    1. Zhan, Xiu-Xiu & Liu, Chuang & Zhou, Ge & Zhang, Zi-Ke & Sun, Gui-Quan & Zhu, Jonathan J.H. & Jin, Zhen, 2018. "Coupling dynamics of epidemic spreading and information diffusion on complex networks," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 437-448.
    2. Gao, Shujing & Teng, Zhidong & Xie, Dehui, 2009. "Analysis of a delayed SIR epidemic model with pulse vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 1004-1011.
    3. Sun, Qingyi & Wang, Zhishuang & Zhao, Dawei & Xia, Chengyi & Perc, Matjaž, 2022. "Diffusion of resources and their impact on epidemic spreading in multilayer networks with simplicial complexes," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Artalejo, J.R. & Lopez-Herrero, M.J., 2011. "The SIS and SIR stochastic epidemic models: A maximum entropy approach," Theoretical Population Biology, Elsevier, vol. 80(4), pages 256-264.
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