Comments on Illustrating differential growth ratesKaiser examines a German video showing the higher transmissibility of the new coronavirus variants.TypePad2021-01-29T07:42:44Zjunkchartshttps://junkcharts.typepad.com/junk_charts/tag:typepad.com,2003:https://junkcharts.typepad.com/junk_charts/2021/01/illustrating-differential-growth-rates/comments/atom.xml/Kaiser commented on 'Illustrating differential growth rates'tag:typepad.com,2003:6a00d8341e992c53ef02788011f541200d2021-02-01T07:29:06Z2021-02-01T20:03:55ZKaiserhttps://www.kaiserfung.comKen: In theory yes. But actual infections are not measurable so the ratio between actual and observed is not known....<p>Ken: In theory yes. But actual infections are not measurable so the ratio between actual and observed is not known. Besides, the ratio is clearly not constant, and depends on factors like testing strategies, and prevalence of disease. Any computation of R is necessarily a lot of assumptions mixed with a low-quality indirect measure of "cases".</p>Ken commented on 'Illustrating differential growth rates'tag:typepad.com,2003:6a00d8341e992c53ef02788011edad200d2021-02-01T04:08:39Z2021-02-01T07:23:39ZKenIt shouldn't matter whether R is actual infections or observed infections provided the ratio between them is constant. If an...<p>It shouldn't matter whether R is actual infections or observed infections provided the ratio between them is constant. If an observed infection produces 2 observed infections should also mean that actual infections produce 2 actual infections. </p>
<p>The paper that discusses the R for the new variant is at https://www.medrxiv.org/content/10.1101/2020.12.30.20249034v2.full.pdf with the interesting results at the end of page 11. This was publishedd in early January so there would be more data now. At that time the difference in R had very wide confidence intervals.</p>Kaiser commented on 'Illustrating differential growth rates'tag:typepad.com,2003:6a00d8341e992c53ef0263e98c3fc3200b2021-01-29T17:05:55Z2021-01-30T00:05:04ZKaiserhttps://www.junkcharts.comDC: Keeping that paper in my archive. It doesn't address the R number as used by the U.K. government, which...<p>DC: Keeping that paper in my archive. It doesn't address the R number as used by the U.K. government, which is a time-varying quantity. Conceptually, I think it means at any sample point of time, given the size of infected population, and the susceptibles, how many susceptibles are being infected on average by each infected person. Of course, no one can measure infections (as opposed to cases), nor can anyone know who does or does not have immunity so any estimate of R is a lot of assumptions plus a little, indirect data. (One of the reasons I don't spend much time talking about R on my blogs.) The way I interpreted R, I'm assuming selecting these time steps in such a way that the only relevant information passed between time steps is the number of newly infected in the previous time step. In other words, the people infected two time steps back are no longer contagious, whether this is due to death or recovery while those infected one time step back are still contagious (on average). </p>Dave C. commented on 'Illustrating differential growth rates'tag:typepad.com,2003:6a00d8341e992c53ef0263e98c3ce6200b2021-01-29T16:11:53Z2021-01-30T00:05:04ZDave C.I have no background in epidemiology, but found this paper helpful: https://calculate.org.au/wp-content/uploads/sites/15/2018/10/spread-of-disease.pdf<p>I have no background in epidemiology, but found this paper helpful:<br />
https://calculate.org.au/wp-content/uploads/sites/15/2018/10/spread-of-disease.pdf<br />
</p>Kaiser commented on 'Illustrating differential growth rates'tag:typepad.com,2003:6a00d8341e992c53ef0263e98c3b8c200b2021-01-29T15:47:00Z2021-01-30T00:05:04ZKaiserhttps://junkcharts.typepad.com/junk_chartsDC: Good question. I assume R is applied at each time step to the new infections of the previous time...<p>DC: Good question. I assume R is applied at each time step to the new infections of the previous time step which means I assumed a built-in recovery/death mechanism. Also, I'm not modeling the end state when the susceptible population tapers away. As far as I know, experts have refused to confirm that there is lasting immunity from infection; some are predicting the disease will become endemic.<br />
It is not clear to me what "R number" is as commonly used. R0, which is the R number at the start when the entire population is susceptible, is the key parameter in the SIR model. So I just interpreted it in the most convenient way so I can show the graphical form. If you know more details about how to interpret R over time, please add to these comments. </p>Dave C. commented on 'Illustrating differential growth rates'tag:typepad.com,2003:6a00d8341e992c53ef02788011564c200d2021-01-29T13:57:24Z2021-01-30T00:05:04ZDave C.Does your graphic assume an infinite "susceptible" population? What about the nature constraints of a limited population, some portion of...<p>Does your graphic assume an infinite "susceptible" population? What about the nature constraints of a limited population, some portion of which has already developed antibodies? </p>