- 1-dose vaccination is 2/3 as effective as 2-dose (consistent with estimates used in Doherty Institute report)
- Vaccination becomes effective after two weeks and does not wane
- All of the population (ages, regions, etc.) is equal in terms of transmission.
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- Vaccination is the only effect on R_eff which is changing in time during this period (9/8/2021 to 22/10/2021 in Vic, 26/6/2021 to 11/10/2021 in NSW).
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Methods:
- R_eff is calculated from a linear regression of ln(new cases) over 8 days (4 days in past to 3 days in future of date of R_eff.
- VET is the inverse of the x-intercept of a linear regression of R_eff(vax).
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Discussion:
- Both vaccination and transmission are inhomogeneously distributed across the population which is likely important! Targeting vaccination to high-transmission groups (age groups, or regions) will cause VET to be overestimated.
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- The age-based roll-out means working-age adults (likely more highly transmitting) were vaccinated later, and this would cause VET to be overestimated.
- Likewise, children <12 (likely less transmitting) were not vaccinated; this also exaggerates VET.
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- "lockdown fatigue" could increase R_eff w/time, leading to an underestimate of VET.
- other changes could be important (e.g. changing weather/seasons, or small changes in public health measures).
- Waning vax effectiveness means VET may be lower than peak after vax.
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- VET is consistent with 86%-93% assumed for AZ/Pfizer by Doherty Institute.
- HOWEVER, due to effects discussed above, I think my VET is more likely an overestimate! Still, I think the observations provide good evidence that vax is effective at reducing transmission.
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Interesting observations:
- Both NSW and Vic appear to show a higher VET (higher slope) just before crossing R_eff = 1. This was noted at the time (e.g. @Chrisbilbo) in that it caused models to overestimate cases, and overestimate date when peak cases would occur.
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- This apparent higher slope just before R_eff = 1, if real, happens at different point in the vaccination rollout in Vic and NSW, and hence is unlikely to be attributed to e.g. vaccination of certain groups, or AZ vs. Pfizer.
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- Vic has consistently shown higher R_eff at a given vax level than NSW.
The cause is not known, but it is NOT a function of vaccination rollout, which is corrected for in this plot! Possible differences are climate, "lockdown fatigue", or LGA-specific settings in NSW.
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- Vic data are also "noisier" (progressing less smoothly in time) leading to larger error in VET estimate for Vic.
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Conclusions:
Vax effectiveness against transmission (VET) is evident in the statistically significant decrease in R_eff with vaccination during lockdown in NSW and Vic.
A simple model gives high VET approx 80-90%, however this is likely to be modestly overestimated.
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NSW and Vic show excellent evidence that vaccine effectiveness against onward transmission is high (>86%)!
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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%
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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%).
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In a recent thread I looked at the performance of some low-covid countries against expectations from models of the expected R_eff achievable at different vaccination levels.
Today let’s examine how jurisdictions in Oceania are doing.
The effective reproductive number R_eff controls whether infections grow (R_eff > 1) or decay (R_eff < 1). We therefore need to achieve R_eff < 1 to have control over the epidemic with our public health and social measures (PHSMs).
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The most important question then, is:
👉"Under what conditions of PHSM and vaccination can we achieve R_eff < 1?"👈
I’ll be plotting R_eff as a function of the effective vaccination expressed as a percentage of total population.
First, comparing the Punaha Matatini and Doherty models is easy. They use very similar methodology. The contact matrix is the same, taken from this paper: journals.plos.org/ploscompbiol/a…
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What that means is that in both models children and the elderly contribute relatively little to transmission, which is driven more by working-age people.
The model from @TonyBlakely_PI of the Population Interventions Unit, released yesterday, comes to some surprising conclusions, for example that Stage 4 lockdowns would continue to be necessary even if 95% 16+ are vaccinated.
I’ve attempted to summarize the differences between the model released yesterday by Melbourne Uni’s Population Interventions Unit (PIU) and the modelling by the Doherty Institute for the National Plan.
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PIU provide a very nice web interface that allows the user to explore the effect of different scenarios on the model outcomes. I encourage you to have a look!
Today we’ll look around the world at countries which have had success at suppressing covid, the delta strain in particular, and see what lessons there might be for Australia.
Some more perspective on the mind-boggling modeling from @BurnetInstitute.
*No country* which has achieved 64% vax of total pop. (equivalent to 80% of 16+) has seen 110 deaths/million population in one month (predicted for VIC in January.
Many countries with high vax, low infection-acquired immunity, and nearly zero restrictions have death rates more than 10X lower (Finland, Norway, Denmark).
Hard to understand why VIC covid deaths should exceed those in other low-covid countries by >10X.
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Burnet Institute predicts VIC will see 11,600 cases/M and 110 deaths/M (deaths 0.93% of cases!) in Jan 2022.
Last month (19 Aug-18 Sep):
UK started at 65% total pop vaxxed, had 14,851 *reported* cases/M and 55.5 deaths/M (deadliest mo. of delta; deaths 0.37% of cases).
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