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Assuming that around half of those cases are infectious and another half carry the new variant, there could be around 25 cases with the new variant in Switzerland. What is the probability that they establish a sustained transmission chain in Switzerland? 4/n
Using branching process models, we can calculate this probability as P = 1 - 1/Re^n where Re is the effective reproduction number and n is the number of initial cases. 5/npic.twitter.com/3JTSlMWGPM
The effective reproduction number in Switzerland is arguably slightly above 1 at the moment. For Re = 1.05, we obtain a probability of 70% that the new variant will spread in Switzerland. For Re = 1.1, the probability would be 91%. 6/n https://sciencetaskforce.ch/epidemiologische-lagebeurteilung-21-dezember-2020/ …
But there is more to it. The equation above assumes that the number of secondary cases are geometrically distributed (k = 1). However, #SARSCoV2 exhibits superspreading and the number of secondary cases is highly overdispersed (k ~ 0.5). 7/n https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.4.2000058 …
That means that many infected cases do not transmit at all, and only a few infected individuals have the potential to initiate a sustained transmission chain. 8/n
Assuming k = 0.5, we obtain a probability of 58% (for Re = 1.05) and 79% (for Re = 1.1) that the 25 cases will initiate a sustained transmission chain in Switzerland. 9/n
So that's still relatively high. However, visitors from the UK (and South Africa) must now go into quarantine in Switzerland. This might prevent some of the potential further spread of the new variant. 10/nhttps://www.bag.admin.ch/bag/en/home/krankheiten/ausbrueche-epidemien-pandemien/aktuelle-ausbrueche-epidemien/novel-cov/empfehlungen-fuer-reisende.html …
Nevertheless, we have to assume that the new variant might start to spread in Switzerland during the coming weeks, particularly because it might have increased transmissibility and therefore a higher Re. End. 11/n
i don't completely follow this equation... doesn't that mean P_ext is decreasing wrt n when Re<1? even if you only infect 0.7 people on average I would've thought more people -> less chance of extinction
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