Well, this is quite extraordinary.
NSW and Vic show excellent evidence that vaccine effectiveness against onward transmission is high (>86%)!
1/
I fit the R_eff vs vaccination data for NSW and Vic to a linear relationship, to get two parameters, the R_eff at zero vax, and the vax effectiveness against onward transmission (VET). The result:
NSW: R_eff(0 vax) = 1.65; VET = 86.1%
Vic: R_eff(0 vax) = 2.27; VET = 86.4%
2/
Solid lines are the Doherty model, linearized:
Doherty uses a transmission matrix which effectively weights some ages more than others in relevance to transmission. I assume vax affects everyone equally. I take a weighted average of VET = 89.7% for AZ (86%) and Pfizer (93%).
3/
Best fits indicate VET is ~86% (close to Doherty 86-93%). NSW and Vic agree very well.
Vic tracks consistently higher than NSW. This is roughly consistent with the difference between Doherty "high" and "medium" PHSM.
4/
NSW: R_eff(0 vax) = 1.65
Doherty "high": R_eff(0 vax) = 1.61
Vic: R_eff(0 vax) = 2.27
Doherty "medium": R_eff(0 vax) = 2.21
We don't know why there is a difference (intrinsic to Syd & Melb? Weather? Lockdown fatigue?)
5/
Conclusions:
1) NSW and Vic data both consistent with a high (86%) vaccine effectiveness against onward transmission in the simplest model.
2) Doherty Inst model was very well calibrated for NSW.
6/
Conclusions cont'd:
3) VIC shows consistently higher R_eff compared to NSW. Vic would be justified in taking a more cautious approach to re-opening. If high R_eff due to "fatigue" then may be OK. If intrinsic to Melb, more restrictions needed after opening.
7//7
Addendum:
VET here is the *overall* vax effectiveness against transmission! (Not "onward")
If vaccine has X eff against infection, Y eff against (onward) transmission if infected, then overall VET = 1-(1-X)(1-Y).
8/7
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