Thread by @haroldpollack

An intentionally over-simplified+bad-graphics nerd-thread with irrelevant math symbols and bad hand-writing inspired by @ADPaltiel, @jasonlschwartz, Amy Zheng+@RWalensky in their recent Health Affairs piece. healthaffairs.org/doi/pdf/10.137…

Today's intentionally over-simplified+bad-graphic nerd moment seeks to explain why we must keep masking, hand-washing+distancing even after we have a good but imperfect vaccine that reduces transmission by some amount gamma--maybe 70%. Why am I using Greek letters? No idea. (2/n)

Suppose people contract COVID+randomly mix w/others lambda times/day. Each time infected+uninfected person meet, Infection is transmitted w/probability kappa. Infectedsleave the population with probability delta/day. Kappa+lambda can be reduced through distancing+masking. (3/n)

Reproduction number R0 is the number of susceptible people an infected person can be expected to infect if you dropped her to randomly mix in a totally susceptible population. In this useful toy model R0=kappa*lambda/delta. When R0<1, we say we have achieved herd immunity (4/n)

If we do the random mixing math in this toy model, it turns out that if we wait long enough, the reduction in population disease prevalence can be written as gamma/[(1-gamma)*R0] (5/n)

If gamma is close enough to 1, we can reach herd immunity. But if R0 is big, the denominator (1-gamma)*R0 is also big+dilute the intervention's long-term impact. For example if R0=10 and gamma=70%, we reduce prevalence, but only about 23 percentage points, 90% down to 67%. (6/n)

What's happening. A 70% reduction in the immediate risk of infection delays many transmission events. But the people we help remain susceptible. The intervention isn't powerful enough to really alter the fundamental ecology and many people are eventually infected. (7/n)

If we can reduce R0 from 10 to (say) 5 through masking and distancing, we would obviously have way fewer infections even before the vaccine is provided. In this case reducing steady-state prevalence from 90% to 80% without any other help. Here's what's less obvious...(8/n)

When R0=10, the vaccine reduces steady-state prevalence from 90% to 66%. When R0=5, the very same vaccine reduces steady-state prevalence from 80% all the way down to 33%. Protective measures that reduce R0 make the vaccine itself much more powerful. (9/n)

This pathetic toy model works better for harm reduction than for distinctive math of vaccines. But the underlying logic is right: Development of (imperfect) vaccines does not diminish importance of mask-wearing+other risk-reduction. These efforts are mutually reinforcing. (10/n)

Tl;dr--The moral of this horribly-written thread: Stay strong everyone. As vaccine is rolled-out, we must redouble our efforts to mask-up, stay home+physically distance. And we must continue effective risk reduction even after an effective vaccine is widely deployed. (11/n)