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. 2022 Jul 6;13:3896. doi: 10.1038/s41467-022-31511-0

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a Birth-death model (BD)^8,9, b birth-death model with Exposed-Infectious individuals (BDEI)^5,10,11 and c birth-death model with SuperSpreading (BDSS)^5,12. BD is the simplest generative model, used to estimate R₀ and the infectious period (1/γ)^8,9. BDEI and BDSS are extended version of BD. BDEI enables to estimate latency period (1/ε) during which individuals of exposed class E are infected, but not infectious^5,10,11. BDSS includes two populations with heterogeneous infectiousness: the so-called superspreading individuals (S) and normal spreaders (N). Superspreading individuals are present only at a low fraction in the population (f_ss) and may transmit the disease at a rate that is multiple times higher than that of normal spreaders (rate ratio = X_ss)^5,12. Superspreading can have various complex causes, such as the heterogeneity of immune response, disease progression, co-infection with other diseases, social contact patterns or risk behaviour, etc. Infectious individuals I (superspreading infectious individuals I_S and normal spreaders I_N for BDSS), transmit the disease at rate β (β_X,Y for an individual of type X transmitting to an individual of type Y for BDSS), giving rise to a newly infected individual. The newly infected individual is either infectious right away in BD and BDSS or goes through an exposed state before becoming infectious at rate ε in BDEI. Infectious individuals are removed at rate γ. Upon removal, they can be sampled with probability s, becoming of removed sampled class R. If not sampled upon removal, they move to non-infectious unsampled class U.