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adamjkucharski's profile
Adam Kucharski
Adam Kucharski
Adam Kucharski
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@adamjkucharski

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Adam KucharskiVerified account

@adamjkucharski

Co-director @LSHTM_CEPR. @WellcomeTrust fellow and @TEDFellow. Author of The Rules of Contagion. Views own.

kucharski.io
Joined January 2012

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    1. Adam Kucharski‏Verified account @adamjkucharski 2 Jun 2020

      I'm getting asked more about the 'k' parameter that describes variation in the reproduction number, R (i.e. describes superspreading). But what does this parameter actually mean? A short statistical thread... 1/

      19 replies . 334 retweets 718 likes
      Show this thread
    2. Adam Kucharski‏Verified account @adamjkucharski 2 Jun 2020

      R measures average transmission per case, but in reality some cases may generate more infection than others, e.g. because of events/places they visit while infectious. So we need a way to estimate variation in R at the individual-level... 2/

      3 replies . 11 retweets 63 likes
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    3. Adam Kucharski‏Verified account @adamjkucharski 2 Jun 2020

      We can do this by fitting a curve to the distribution of secondary infections, and see how much variation there is. A commonly used tool is the negative binomial distribution, which has mean=R and variation captured by a dispersion parameter 'k' https://www.nature.com/articles/nature04153 … 3/

      1 reply . 15 retweets 74 likes
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    4. Adam Kucharski‏Verified account @adamjkucharski 2 Jun 2020

      If k is very large, every case generates transmission randomly at constant rate with mean=R (i.e. equivalent to a Poisson process as k->infinity). Here's what the distribution of transmission looks like when R=3, k=1000 (dashed line shows R). 4/pic.twitter.com/3kCIpmoiBC

      2 replies . 13 retweets 63 likes
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    5. Adam Kucharski‏Verified account @adamjkucharski 2 Jun 2020

      If k is smaller, then there is more variability - some cases generate a lot of new infections, while most generate very few. Here's the negative binomial distribution when R=3, k=0.2 (plausible for COVID, SARS). Note x-scale is cropped at 20, but can obviously go higher 5/pic.twitter.com/Dw7MgnVEFj

      4 replies . 15 retweets 56 likes
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    6. Adam Kucharski‏Verified account @adamjkucharski 2 Jun 2020

      So how do we calculate k? One way is to estimate directly from transmission chains reconstructed from contact tracing data, e.g. https://www.researchsquare.com/article/rs-29548/v1 … 6/pic.twitter.com/eqqSuMMD7Z

      3 replies . 14 retweets 79 likes
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    7. Adam Kucharski‏Verified account @adamjkucharski 2 Jun 2020

      Alternatively, we can estimate k from the distribution of outbreak sizes after infections are introduced to a new location, using a simple transmission model: https://wellcomeopenresearch.org/articles/5-67  7/

      2 replies . 13 retweets 56 likes
      Show this thread
      Adam Kucharski‏Verified account @adamjkucharski 2 Jun 2020

      As 'k' is a bit hard to interpret directly, we can also use it to calculate what proportion of infections generate a given amount of transmission, e.g. does transmission follow something like a '20/80 rule'? Here's a conversion table for R=3... 8/8pic.twitter.com/Y9ho4Vs82v

      1:39 am - 2 Jun 2020
      • 29 Retweets
      • 123 Likes
      • Na Sirf Musiqi 🧡 FVM 🇺🇦 Zoë McLaren, PhD Henrique Antoun The Real McCoy 🔬Samantha Yammine, PhD Alex Harrowell Δημήτρης Δαλαγιώργος 🇪🇺🇬🇷🇺🇦 Matt Bond
      18 replies . 29 retweets 123 likes
        1. Dan Grey‏ @dan_grey 2 Jun 2020
          Replying to @adamjkucharski

          So... As a practical conclusion, this suggests that maintaining social distancing really matters, doesn't it? If an individual drops that precaution, they can become a "super-spreader" if they become infected. Someone who maintains social distancing wouldn't.

          0 replies . 0 retweets 1 like
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        2. Ewan Birney‏ @ewanbirney 2 Jun 2020
          Replying to @adamjkucharski

          Adam, as you know, I do wonder if bimodal / multi-distribution "r" is right (of course, r in some sense is just some integer number in each case - it is how we model r which is the interesting question in the classic all models are wrong, some are useful)

          1 reply . 0 retweets 1 like
        3. Ewan Birney‏ @ewanbirney 2 Jun 2020
          Replying to @ewanbirney @adamjkucharski

          Viral genomics I think also can inform here, and then also if we can get better location / context of transmission events, and these "high k" or "super-spreading" events might well be location specific then we can both build better models can - critically - target NPI better.

          2 replies . 0 retweets 2 likes
        4. Show replies
        1. JW‏ @jscotland1990s 2 Jun 2020
          Replying to @adamjkucharski

          Surely it’s good news if K lower as we come off peak of Covid? As then only 9% need to become immune to stop the rapid spread- or is that all too simple?

          0 replies . 0 retweets 0 likes
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        1. Ritwik Priya‏ @ritwik_priya 2 Jun 2020
          Replying to @adamjkucharski

          What is the k implied by the assumptions of your model (Poisson-ish contact distribution convoluted with binomial infectivity) on the contact tracing/ isolation effectiveness paper?

          0 replies . 0 retweets 0 likes
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        1. William‏ @William60378254 2 Jun 2020
          Replying to @adamjkucharski

          People are getting overexcited by k. It's a function of people's behaviour. Initially most people were careful so k was quite low. Over time, k will rise closer to influenza.

          0 replies . 0 retweets 1 like
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        1. Stacey Auger‏ @staceyauger1 2 Jun 2020
          Replying to @adamjkucharski

          Because Math has imaginary numbers... the rest of us have to pretend to understand. K + Ro might be dating but their not likely to reproduce and so - help. We do want to understand 🙄

          0 replies . 0 retweets 0 likes
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        1. Marmaduke Jinks  🏴󠁧󠁢󠁷󠁬󠁳󠁿‏ @marmadukejinks9 2 Jun 2020
          Replying to @adamjkucharski

          Still is subjective.

          0 replies . 0 retweets 0 likes
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        1. JohannesBorgen‏ @jeuasommenulle 2 Jun 2020
          Replying to @adamjkucharski

          Hi Adam, have you read the work of @gro_tsen about about that parameter (or more generally the variance of contact PD) has a dual role (in terms of extinction proba vs final attack rate) when you look at spreader vs receivers distribution ? Really fascinating

          0 replies . 0 retweets 0 likes
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        1. Keith Head‏ @ckhead 2 Jun 2020
          Replying to @adamjkucharski

          For a given estimate of R, does the herd immunity rate fall with k? is there an analytical relationship?

          0 replies . 0 retweets 0 likes
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