Random graph and epidemiology people, I have a question for you: what is the marginal probability of indirectly killing someone by going out without a mask? There is a small probability I get infected, and then a small probability I infect other people, which in turn...
The impact of my choice looks exponential, but the likelihood is small. Is there a way to calculate it?
I have too many friends who are getting ready for apero from May 11. I want to tell them how many people they will indirectly kill.
(I feel like a mean field approach is easier to use, but it doesn't quantify the consequences of one given person.)
Allright, I calculated it myself, with back of the enveloppe simulations. I'll present it tomorrow. Spoiler: stay at home.
Alright, so let’s go. (TW: armchair epidemiologist here). Here is my attempt to calculate the marginal effects of being infected. I’ll present all the steps of the model, so you can clearly see all the assumptions (mean-field, non spatial, non structured, etc).
With parameters reasonable for Covid-19: R0 = 2 (Reproduction number), γ = 0.2 (Recovering rate), λ=0.01 (1% Death rate). I consider a population of 100000 people (like a city, or a large neighborhood), starting with N0=1000 infected.
I run SIR simulations, and I consider that the number of death is λ*number of recovered.
SIR gives this trajectory: it ends up with 800 deaths and 78888 recovered (immune).
My initial question was: what is the consequence of going out without a mask? Let’s break up this question in two:
- What if the probability of getting infected?
- How many people will I indirectly kill if I get infected?
At time t=0, there are S=N-N0 susceptibles, I=N0 infected, R=0 recovered. At time t=1 day, there will be βIS/N fewer susceptibles, βIS/N-γI more infected, and γI more recovered, including more λ*γ*I deaths. (That's the SIR model)
For a susceptible, the probability of getting infected is the number of newly infected divided by the number of susceptibles: βN0/N. It looks good: the more infected people(=contagious), the more likely to get infected.
Now what about the consequence of being infected? If I get infected, I will transmit the disease to R0 people, by definition of the model. These people will in turn infect others, etc. A λ-fraction of these people will die.
If the epidemic starts with N0=1000 infected, there will be X deaths after T days. But if the epidemic starts with N0=101 infected, there will be X’ deaths after T days. I want to measure X’-X, the number of deaths that are related the one extra initial infected person.
I choose T to be as such X’-X is maximal.
X’-X at 0 (because X’=X=0 at first), peaks, and goes back to zero. The final state of SIR is nearly independent of initial conditions. The same number of people will die eventually. The question is how high it peaks #flattenthecurve.
Now the results. I decided to present the results as a function of N0, the number of initial infected. The effect of an extra infected individual is not the same if there are very few cases or if there are infected people everywhere. First, the likelihood of getting infected:
The number of extra deaths at the peak:
Now the combined result (the product of the two last graphs): the expected number of deaths caused by someone getting out without a mask.
Conclusion: This is a very basic model (again, #armchairepidemiologist), I wish I could make it more realistic. I understand one needs to go out to work/buy groceries/etc. That’s fine as long everyone is making their best to protect each other.
If not protected, with R0=2, the effect of going out is (indirectly) killing 0.0006 people. Again, that's the marginal effect, for one person, going out for one day. Now you know.
I believe it would be useful to publicize more widely the impact of going out without a mask, and more generally the marginal expectancy of measured quantities, to raise awareness about individual responsibility. Reopening does NOT mean "going back to normal". #keepstayinghome
One extra note:
- individual consequence of going out: probability of getting infected (1% for N0=1000) x death rate of the disease (1%). That 0.01% of one death (of oneself).
- collective consequence of going out: 0.1% of a death.
Interestingly, the former increases with N0, while the latter remains nearly constant with N0. People will stop going out if the number of cases outside is too high because the individual risk is too high. But the collective risk starts already at a very low number of cases.
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À l'occasion de la publication de ce livre, je me dis qu'il est tant de raconter une anecdote qui date de mars 2020. Quinze mois plus tard, il y a prescription, Yanis ne m'en voudra pas.
Le 17 mars, Raoult (et ses collègues) publie le fameux article sur son traitement à l'hydroxychloroquine. Je prends le temps de le lire et de relever toutes les erreurs statistiques, etc. Dans la foulée, l'IHU publie des papiers presque tous les jours.
Je regarde notamment ce papier hallucinant, "La peur contre les données" qui cherche à démontrer qu'on meurt davantage d'un rhume que du Covid-19. pubmed.ncbi.nlm.nih.gov/32201354/.
Je publie un thread qui a son petit succès. J'interpelle son premier auteur, Yanis Roussel, sur Twitter.
I believe #EmilyInParis viewers should know a historical fact about where she lives: Place de l'Estrapade.
It's located in the Fifth Arrondissement, in the Quartier Latin, one of the oldest neighborhoods in Paris.
Until 1687, this cute little place hosted an 'estrapade', or 'strappado', a torture instrument that is not exactly Instagram-friendly.
It consisted in suspending the victim by a rope tied to the wrists, behind their back, resulting in dislocated shoulders.
To speed up death (and/or to make it more dramatic), a layer of sadism was added: the rope was released then abruptly blocked just before the victim touched the ground, leading to further pain and dislocation. #EmilyInParis
A friend asked me why the number of cases is increasing while the reproduction number (R) is stable.
The answer is obvious for someone who is used to concepts like functions, curves, derivatives, primitives.
For others, it's impenetrable.
I'm not going to make a long thread out of it, but a simple comparison:
- In a car, when you press the gas pedal, you move forward. More precisely: you accelerate.
- The position of the car increases, the speed of the car increases, the acceleration is constant.
If you barely release the gas pedal, the position will continue to increase (the car is still moving), the speed still increases, however the acceleration remains constant but at a lower level.
Un ami vient de me demander pourquoi le taux de positivité augmente alors que le R est stable.
La réponse est évidente pour quelqu'un qui a l'habitude manipuler des courbes, des fonctions, des dérivées, et des primitives.
Pour les autres, c'est incompréhensible.
Je vais pas en faire un long thread, mais une simple comparaison.
- En voiture vous appuyez sur l'accélérateur, vous avancez, et plus précisément : vous accélérez.
- La position de la voiture augmente, la vitesse de la voiture augmente, l'accélération est constante.
Si vous relâchez à peine l'accélérateur, la position continuera à augmenter (la voiture roule toujours), la vitesse augmente encore, par contre l'accélération est constante mais plus faible.
Instant veille journalisme US:
Une éditrice du Guardian US fait un grand appel pour trouver de nouvelles plumes, via Twitter, et propose de skyper avec des freelances pour discuter. Des centaines de réponses.
Depuis quelques temps les chroniqueurs du NYT discutent pendant une heure sur Periscope après la publication de leurs chroniques, avec questions/réponses. Ça permet de voir le travail de fond qui est fait (c'est souvent des chroniques très argumentées).
Il existe une page sur le site du NYT qui rassemblent toutes les corrections : nytimes.com/section/correc…
Avec également la liste des articles (et tribunes) concernés.
Il faut se rendre compte du niveau de méticulosité.
Oh, I found the names of the two editors of the next issue of Advances in Genetics, called "Cosmic Genetic Evolution": they are Edward Steele and N. Chandra Wickramasinghe, who are, hum, respectively first and last authors of that paper.