Israel is currently (early January 2020) vaccinating at a sustained rate of 1% of the population per day; no other country comes close to this rate. To reach the usually quoted level of the herd immunity and 95% efficacy, i.e. to bring R to 1 in absence of any other control measures, they will need to get to about 74%; 2 doses mean 150 days or 5 months. This brings us to May, if we can keep the rate going (and such public health campaigns often slow down later on) but only results in R=1 (under the assumption of no lockdowns) and assumes high and uniform efficacy.
Where does 74% calculation come from? Assume 
is the efficacy and 
is the estimate of the basic reproductive number – the rate at which new infections are produced in the absence of any additional control measures. Then, 
, the proportion of the population that needs to be vaccinated to bring the effective reproductive number, 
, to 1 is
![\[ p=\frac{1}{x}\times\left( 1-\frac{1}{R_0} \right)\]](https://statisticallyinsignificant.blog/wp-content/ql-cache/quicklatex.com-e469585cdb2093ca935407a04c1967af_l3.png "Rendered by QuickLaTeX.com")
(check Marc Lipsitch’s blog linked above).
If we want to eradicate the virus and later to prevent it from reinvading, we will need to go well beyond 74%; also, spacing the two doses more almost certainly means lower efficacy. All of these requires a higher % of the population and hence takes longer.
With the new variant possibly adding about 0.9 to 
and Astra Zeneca vaccine efficacy of 70%, the above formula yields 
meaning that it is not possible to stop the disease from spreading without additional non-pharmaceutical measures like lockdown applied long term.
On the positive side, if we keep applying lockdowns and use masks, we should see the results earlier, as we will need to target the effective and not the basic . This in turn might actually slow down the vaccine roll out and uptake – so important to deal effectively with expectations.
The strategy also depends on what we use the vaccine for. The current use seems not to target eradication, but to release the pressure on NHS and to protect the vulnerable. This might be achieved earlier with a combination of lockdowns, masks, and test and trace.
It is important to realise that these things do take time and it is irresponsible of the politicians to promise a quick fix. The epidemic will not be over by Easter, but we might start seeing some results with vaccine combined with lockdowns. Even more important is to build up trust, between decision-makers, medics, scientists and the public. And trust currently seems to be in short supply.