Speaker
Description
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 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 $R_0$, 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 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. Finally, we illustrate several data-driven epidemic scenarios, assuming that infectiousness varies only across phases, each displaying high variability in its respective generation time. \cite{ripoll_generation_2026}, \cite{ripoll_discrete_2023} and \cite{breda_efficient_2021}.
Bibliography
@article{ripoll_discrete_2023,
title = {A Discrete Model for the Evolution of Infection Prior to Symptom Onset},
volume = {11},
issn = {2227-7390},
url = {https://www.mdpi.com/2227-7390/11/5/1092},
doi = {10.3390/math11051092},
language = {en},
number = {5},
urldate = {2026-02-28},
journal = {Mathematics},
author = {Ripoll, Jordi and Font, Jordi},
month = feb,
year = {2023},
pages = {1092},
}
@article{breda_efficient_2021,
title = {Efficient numerical computation of the basic reproduction number for structured populations},
volume = {384},
issn = {03770427},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0377042720304568},
doi = {10.1016/j.cam.2020.113165},
language = {en},
urldate = {2026-02-28},
journal = {Journal of Computational and Applied Mathematics},
author = {Breda, Dimitri and Florian, Francesco and Ripoll, Jordi and Vermiglio, Rossana},
month = mar,
year = {2021},
pages = {113165},
}
@misc{ripoll_generation_2026,
title = {Generation time in a discrete epidemic model with asymptomatic carriers: beyond geometric waiting times},
journal = {Preprint},
author = {Ripoll, Jordi and Saldaña, Joan},
year = {2026},
}
