Generation time in a discrete epidemic model with asymptomatic carriers: beyond geometric waiting times

TL;DR

This paper models the distribution of generation times in infectious disease transmission, incorporating asymptomatic carriers and variable infectiousness across different disease stages using a non-Markovian discrete-time framework.

Contribution

It introduces a recursive non-Markovian model capturing variable infectiousness and derives the generation time distribution from basic epidemiological parameters.

Findings

Expected generation time is a convex combination of pre- and post-symptom onset times.

The n-th moment of generation time relates to moments of weighted forward recurrence times.

Most diseases, except measles, show moderate variability in generation time distribution.

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, except measles, exhibits moderate variability in its respective generation time distribution.