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A stochastic epidemic model with two quarantine states and limited carrying capacity for quarantine

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  • Amador, J.
  • Gómez-Corral, A.

Abstract

We study extreme values in an SIQS (susceptible → infectious → quarantined → susceptible) model with two different states for quarantine, termed quarantined susceptible and quarantined infective, and limited carrying capacity for the quarantine compartment. The aim is to characterize the probability distribution of various stochastic descriptors, such as the random length of an outbreak, the time until the quarantine compartment is full for the first time, the maximum number of simultaneously quarantined individuals, and the maximum number of simultaneously infected individuals during an outbreak. For illustrative purposes, a numerical study of the model is performed to show the influence of certain key parameters on the spread of a disease amongst a homogeneously mixing community of individuals.

Suggested Citation

  • Amador, J. & Gómez-Corral, A., 2020. "A stochastic epidemic model with two quarantine states and limited carrying capacity for quarantine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    • Handle: RePEc:eee:phsmap:v:544:y:2020:i:c:s0378437119311185
    DOI: 10.1016/j.physa.2019.121899
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    References listed on IDEAS

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    1. Clancy, Damian, 2014. "SIR epidemic models with general infectious period distribution," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 1-5.
    2. Zhang, Xiao-Bing & Huo, Hai-Feng & Xiang, Hong & Shi, Qihong & Li, Dungang, 2017. "The threshold of a stochastic SIQS epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 362-374.
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    5. Economou, A. & Gómez-Corral, A. & López-García, M., 2015. "A stochastic SIS epidemic model with heterogeneous contacts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 78-97.
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    Cited by:

    1. Utsumi, Shinobu & Arefin, Md. Rajib & Tatsukawa, Yuichi & Tanimoto, Jun, 2022. "How and to what extent does the anti-social behavior of violating self-quarantine measures increase the spread of disease?," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Gómez-Corral, A. & Lopez-Herrero, M.J. & Taipe, D., 2023. "A Markovian epidemic model in a resource-limited environment," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    3. Babaei, A. & Ahmadi, M. & Jafari, H. & Liya, A., 2021. "A mathematical model to examine the effect of quarantine on the spread of coronavirus," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Antonio Gómez-Corral & Martín López-García & Maria Jesus Lopez-Herrero & Diana Taipe, 2020. "On First-Passage Times and Sojourn Times in Finite QBD Processes and Their Applications in Epidemics," Mathematics, MDPI, vol. 8(10), pages 1-25, October.
    5. Ammar Yasir & Xiaojian Hu & Munir Ahmad & Abdul Rauf & Jingwen Shi & Saba Ali Nasir, 2020. "Modeling Impact of Word of Mouth and E-Government on Online Social Presence during COVID-19 Outbreak: A Multi-Mediation Approach," IJERPH, MDPI, vol. 17(8), pages 1-21, April.

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