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athowes / exp-growth

Time-series methods for disease-agnostic metagenomic environmental threat detection
https://athowes.github.io/exp-growth
MIT License
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Increased transmissibility and global spread of SARS-CoV-2 variants of concern as at June 2021 #7

Closed athowes closed 1 year ago

athowes commented 2 years ago

https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2021.26.24.2100509

The appendix.

athowes commented 2 years ago

Summary of "Supplementary Text 1: Estimating growth rates"

The number of infections for variant $v$ is governed by

$$ I_v(t) = I_v(0) e^{r_v t} $$

where the variant-specific growth rate can also be defined in terms of a wild-type growth rate and a transmission advantage

$$ rv = r{wt} + \Delta_v $$

The chance of a randomly sampled sequence $S_i$ at time $t_i$ being of type $v$ is

$$ P(S_i = v) = I_v(t_i) / \sum_k I_k(t_i) $$

They manage to frame this as a multinomial logistic regression where you learn $\Delta_v$ for each variant (so I guess it's a baseline category with wild-type as baseline). They used nnet.

I think this is the same model as the one Charlie was using and also suffers from just being lines on the log-odds scale.

athowes commented 2 years ago

See also "Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England" (Science)