D.2 What do we mean by population immunity? And why does it matter?

In a population that so far has had negligible natural infection, we define population immunity as the ‘average vaccine effectiveness (VE) by time, allowing for the number of people vaccinated and the time since they were each vaccinated’.

This definition might be for the average VE protection against death, against hospitalisation, against symptomatic disease or against getting any infection (be that asymptomatic or symptomatic). These distinctions are important because:

• VE immediately after completing the primary course (or booster) can differ for protection against death through to that against any infection; and
• VE can wane by time since completion of the primary course (or booster).

Consider a simple example of a vaccine that gives (on expectation) a 90 percent reduced risk of being hospitalised one month after completion of the primary course, 80 percent protection two months later, 70 percent protection three months later, and 60 percent four months later. Imagine a country of ten people in which three were vaccinated one month ago, three were vaccinated two months ago, three were vaccinated three months ago, and one is unvaccinated. The average VE is (3×90 percent + 3×80 percent + 3×70 percent) / 10 = 72 percent. If this country opened to the world at this point, and the entire population was infected quickly (putting aside protection against any infection for now), we would expect a hospitalisation rate 72 percent lower than if no one had been vaccinated.

Now imagine that the tenth and last citizen has decided to get vaccinated. The primary course is just one dose, and it takes one month to get their immunity or VE of 90 percent. After that month, the average VE of population immunity will be (1×90 percent + 3×80 percent + 3×70 percent + 3×60 percent) / 10 = 72 percent. That is, no difference from a month ago, because the gain of the one person getting vaccinated is offset by the loss of immunity among the nine vaccinated people after another month of waning. Accordingly, this nation of ten people could have lifted its restrictions a month earlier: there is no difference in expected health loss from having one month less of isolation.

This simple example was just for protection against hospitalisation. The situation becomes more complex if we factor in protection against any infection, since the health loss is a function of both the reduced transmission risk and infection level, and the reduced risk of being hospitalised among those infected (both unvaccinated and vaccinated if there is less than 100 percent protection against any infection).