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<p>Non-Markovian theory provides the most accurate stochastic description of an infection spreading on a contact graph with a general distribution of the infection time and curing time. However, the infection time is not directly measurable and instead the generation time is measured in real-world epidemics. Here we show that if the generation time follows approximately a Weibull distribution with shape parameter <i>α</i>, then the Weibull infection time of the spreading process possesses a similar shape parameter <i>α</i>. For a large list of published generation times in biological, mainly respiratory epidemics, the Weibull shape parameter <i>α</i> is computed, which reveals that nearly always <i>α</i>&#xa0;&gt;&#xa0;1. The impact of this observation is that a complicated non-Markovian analysis is not needed, because the well-established Markovian case <i>α</i>&#xa0;=&#xa0;1 provides a lower bound for the epidemic threshold and an upper bound for the basic reproduction number and the nodal infection probabilities in the contact graph.</p>

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Classical mean-field epidemic theory upper-bounds real disease spread

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月23日

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  • Brian L. Chang,
  • Piet Van Mieghem

摘要

Non-Markovian theory provides the most accurate stochastic description of an infection spreading on a contact graph with a general distribution of the infection time and curing time. However, the infection time is not directly measurable and instead the generation time is measured in real-world epidemics. Here we show that if the generation time follows approximately a Weibull distribution with shape parameter α, then the Weibull infection time of the spreading process possesses a similar shape parameter α. For a large list of published generation times in biological, mainly respiratory epidemics, the Weibull shape parameter α is computed, which reveals that nearly always α > 1. The impact of this observation is that a complicated non-Markovian analysis is not needed, because the well-established Markovian case α = 1 provides a lower bound for the epidemic threshold and an upper bound for the basic reproduction number and the nodal infection probabilities in the contact graph.