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The spreading time in SIS epidemics on networks

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  • He, Zhidong
  • Van Mieghem, Piet

Abstract

In a Susceptible–Infected–Susceptible (SIS) process, we investigate the spreading time Tm, which is the time when the number of infected nodes in the metastable state is first reached, starting from the outbreak of the epidemics. We observe that the spreading time Tm resembles a lognormal-like distribution, though with different deep tails, both for the Markovian and the non-Markovian infection process, which implies that the spreading time can be very long with a relatively high probability. In addition, we show that a stronger virus, with a higher effective infection rate τ or an earlier timing of the infection attempts, does not always lead to a shorter average spreading time E[Tm]. We numerically demonstrate that the average spreading time E[Tm] in the complete graph and the star graph scales logarithmically as a function of the network size N for a fixed fraction of infected nodes in the metastable state.

Suggested Citation

  • He, Zhidong & Van Mieghem, Piet, 2018. "The spreading time in SIS epidemics on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 317-330.
    • Handle: RePEc:eee:phsmap:v:494:y:2018:i:c:p:317-330
    DOI: 10.1016/j.physa.2017.12.048
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    References listed on IDEAS

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    1. Dickson, David C.M. & Waters, Howard R., 2002. "The Distribution of the time to Ruin in the Classical Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 299-313, November.
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    3. Draief, Moez, 2006. "Epidemic processes on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 120-131.
    4. Artalejo, J.R., 2012. "On the time to extinction from quasi-stationarity: A unified approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(19), pages 4483-4486.
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    Cited by:

    1. He, Zhidong & Van Mieghem, Piet, 2020. "Prevalence expansion in NIMFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. Wu, Qingchu & Zhou, Rong & Hadzibeganovic, Tarik, 2019. "Conditional quenched mean-field approach for recurrent-state epidemic dynamics in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 71-79.

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