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This study develops a mathematical model to calculate the probability distribution of generation time (the interval between successive cases in a transmission chain) for infectious diseases with asymptomatic carriers. The model accounts for variable infectiousness across three disease stages: latent, asymptomatic, and symptomatic, using non-geometric waiting time distributions. The researchers demonstrate that the expected generation time is a weighted average of generation times before and after symptom onset, with weights determined by infectiousness levels at each stage.
Why it matters
Understanding generation time distributions is critical for predicting epidemic spread and evaluating public health interventions. This model provides a more realistic framework than previous approaches by incorporating asymptomatic transmission and variable infectiousness over time, which is particularly relevant for diseases like COVID-19 where asymptomatic carriers play a significant role in transmission.
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⚠️ Preprint – Noch nicht peer-reviewed
Dieser Artikel wurde noch nicht von unabhängigen Experten begutachtet. Die Ergebnisse sind vorläufig und sollten mit Vorsicht interpretiert werden.
Abstract: We study the random times between successive cases in a transmission chain of infectious diseases with asymptomatic carriers. We derive the probability distribution of this generation time (in days) from a discrete-time epidemic model with variable infectiousness both along elapsed times and across phases. The introduced non-Markovian model is a compact recursive system featuring random waiting times at each of the three infected stages: latent, asymptomatic, and symptomatic. By rearranging the terms of the basic reproduction number, which represents the expected number of secondary cases produced by an asymptomatic primary case who may eventually develop symptoms, we get to the generation-time probabilities. The expected generation time is a convex combination of the expected generation times before and after the onset of symptoms. Additionally, our analysis reveals that the n-th moment of the generation time is related to the moments up to n-th order of the weighted forward recurrence time at each phase and the moments up to n-th order of the latent period and the incubation period. These weights are the infectiousness along the elapsed times for each transmission phase. Finally, we illustrate several data-driven epidemic scenarios, assuming that infectiousness varies only across phases and discrete Weibull distributions for the waiting times. Each disease analyzed shows a range of variability in its generation time distribution, from low to moderate.