Laurent Schirrer’s original tweet transcript
26 March 2020, 22:19
Two ways one can contribute to fight #covid19 : 1/ #stayathome ! 2/Offer your pro competences. My bckgrnd is physics modelling, so I naturally became interested in #epidemy models in past few weeks. Here below my first modest contribution: notes on a recent @UniofOxford paper…
The paper was revealed by @FT on 24/3 in these misleading terms “Coronavirus may have infected half of UK population — Oxford study”. Misleading because it’s all in these 3 letters: “may”.
Authors modelled UK cumulative #covid19 death series using simple #SIR mathematics (accessible to “anyone” with maths knowledge), parameters taken from papers. Only technicity was the probabilistic framework – simpler direct models would have got to same conclusion as I will show
@lourenco et al only objective was to demonstrate the need for urgent serological testing so one can answer the question: how many infected in UK as of today ?
They did this by demonstrating the IMPACT of an unknown parameter they called rho: the % of population that is at risk to develop a severe disease. rho is currently not accessible to experience, because the number contacted by the virus is not measured.
IMPACT according to paper ? See this
The model is asked to reproduce the (unfortunately) only reliable data we have: the cumulative number of dead, called Lambda(t). According to different values of rho, the model predicts very different situations with respect to the current (19/3) number of infected.
rho=0.001 means 1 person out of a thousand will develop severe form if infected. In such case, more than 60% of UK population would be infected. In the case of high rho=0.1, not many infectious people are needed to explain the same number of deaths…
To know more about what experts think of the approach taken by @UniofOxford paper, read: https://www.sciencemediacentre.org/expert-reaction-to-paper-on-33-wuhan-babies-born-to-mothers-with-covid-19/
Personaly, I got very convinced by the approach taken to model the cumulative death rate. But I also developed the intuition that this paper could be pushed further. Obviously, authors had restricted themselves to not appear “predictive”. It was not their scope.
But I did dare doing it. Models are made to forecast. If not, what is their use ? So, I took an Excel sheet, coded a clone of the model and here it is. My model gets to same conclusions as the original, but can explore the future. Hence additional insights and questions.
Here below these new insights and my conclusions. I am currently looking for a contributor able to code in R or Python to carry additional sensitivities. I will start with my model’s limitations. They do not impact my remarks, I believe.
1- The model has a very simplified way to solve differential equations. Hence I’m not confident in the time prediction aspect of the y(t) curve “peak”. My next step is get s-o help me use a R code same as the excellent one provided by @jameshay218 (a professional researcher).
2- The derivative of death curve in log scale is beta.y(1-z)/z[t-psi] * I need to peer review this please. The second term is constant. In such case, the slope of death curve simply reflects Ro. Ro is uniquely determined, it could have been removed from @LourencoJML paper.
(FYI I found UK and Italy Ro =2.75. The limits of not being a professional is I do not have time to read all published evidence but would be interested to know :). I give these values subject to my model coding being right, as this could affect term 2 of equation)
3- Forecasting death rate. Beyond model results, the equation published by Oxford is L(t)=N.rho.Theta.z(t-psi). It simply means that moving from rho=0.001 to rho=0.1 gives death toll 100 times bigger. An even stronger argument in favour of launching serology test campaign.
4-Forecasting death rate for #Italy. The benefit of manipulating models lies in the knowledge it gives of the physical system itself. Based on previous comment on Ro and initial slope, I interpret that confinment and early measures have saved many,many, lives.
The above model: Italy; Ro=2.75; rho=2e-3; most interesting observation is from 13 march, death toll deviates from model which I interpret: either simple SIR is not applicable to such complex epidemic system, or “Ro got lower” (confinment). Either way: #lockdown saved lives.
And if you are not convinced. Ro=2.75; rho=0.1 matches the data equaly well for the start of the curve. Death toll, yes, 1M in a do nothing scenario. Remember rho is totally uncertain, not resolvable from modelling (though rather too high here to be realistic).
5- #SIR models explain #herdimmunity concept. The disease does not stop because there are no more people to be infected, but because the rate of new infections is dying out. Unfortunately the higher Ro (e.g. 2.75) the more people infected at the end.
To take this work further, I need contributors to make my model fool proof. Thereafter, we can look into ways to add more complex physics. My feel is science community can get more out these models than is currently published. The effort is worth it, this crisis has no precendent
PLOT CURVES. Left Axis population proportion. GREEN s=susceptible; BLUE y= infected; RED r= recovered or dead (r=z-y); Right Axis numbers in log scale. PURPLE L cumulative dead, L obs real (from JHU data base).
29 March 2020
This week-end I coded my model using “R” with exact differential eq. solutions. Ref: @jameshay218
The model validates the preliminary Excel version and all of the above. I confirm the model is NOT predictive for ultimate death curves. Here a dashboard of Excel version Germany.
1 April 2020
My work continues with friends and collaborators on @CovModel . Looking for pro peer reviewer and collaborators on various tasks