Except, the chance of receiving infection is already chance of being tested positive, and thus you cannot multiple it twice.
In case R0=6 without controk neasure it will transmit like this:
With vaccine stopping 64% infection it will goes like this:
Much better, but still increasing exponentially
Please simulate contacts
Unvaccinated with unvaccinated has your first progression 1 to 6 to 36 to 216, that we can agree on.
Vaccinated has a much lower change of exposing a vaccinated enough to infect them. (Lower viral load.)
1 to 0.7776, higher if they are around each other a lot.
You are making the assumption a vaccine only protects the individual from infection.
Strong evidence a vaccine reduces the chance of infecting another person:https://medicalxpress.com/news/2021-05- ... ssion.html
One dose:It found immunization with either the Pfizer or AstraZeneca vaccine reduced the chance of onward virus transmission by 40-60%. This means that if someone became infected after being vaccinated, they were only around half as likely to pass their infection on to others compared to infected people who weren't vaccinated.
After two doses, a 90% reduction in transmission for AZ and Pfizder:https://www.verywellhealth.com/cdc-stud ... es-5121080
Now, as before the risk of infection was about the risk of transmission, I assumed the same. It is possible for a vaccine, like AZ is, to be more effective stopping transmission than preventing the person inoculated from being infected.
This is why a 50% effective rate is acceptable for a vaccine. What is unusual with Covid19 is with attenuated virus vaccines, the transmission remains high.
All of the adreno virus vaccines (AZ, J&J, Sputnik V) and mRNA (Moderna, Pfizer) are amazingly good at stopping transmission.
Theoretically, you could have a vaccine where 90% of the people were infected (10% effective) and yet they do not pass on the virus (unlikely, I admit, but theoretically possible).
It isn't Ro*effectiveness it is Ro* (1-%transmit)*(1-%receive). You are assuming 100% of the vaccinated who get the virus produce enough virus to infect someone else. Thankfully, we are not in that dooms day scenario. If that were the case, the UK, US, Israel, and others would have much steeper growth curves.
Individuals care about how much a vaccine protects them.
Health authorities care how much a vaccine prevents transmission.
Now, the two tend to be correlated, but with Covid19, not so much.
AZ does much better preventing transmission than it does preventing infection. Ok, great from a health authority perspective.
SinoVac and SinoPharm seem to have little benefit in transmission. I speculate this is why Chile and the UAE are doing far worse from a virus infection standpoint than their vaccination rates suggest. https://ourworldindata.org/explorers/co ... BR~QAT~AREhttps://ourworldindata.org/explorers/co ... by+dose%29
I've done a very amateur model of virus propagation and modified it for delta and vaccine effectiveness. Now, I make assumptions on how well natural immunity after a prior infection works and how fast it fades away, but the virus would be spreading far faster if every one who caught it was that infectious. In particular the high fraction of asymptomatic.
We'll be ok with a higher level of vaccination. I calculate with pretty darn high levels.
Think, the Measles vaccine is only 97% effective with an Ro of 50! (most contagious disease I know about). The population is far from fully vaccinated, yet it dies off (ok, it came back..., but people stopped vaccinating as it became so rare). There is another aspect which is people do not transmit as much if vaccinated. https://www.cdc.gov/vaccines/vpd/measles/index.html
I doubt I'll convince anyone. While I have my concerns on this virus, it needs to be in perspective.