R0 Is Not All that Matters

I previously posted about ‘Why R0 Matters,” explaining that R0 (that’s “R-zero” or “R-naught”) is medicine’s measurement of how infectious a pathogen (such as a virus) is in a host population.   In the current Wuhan Coronavirus outbreak (2019-ncov), much press coverage is mentioning that scientists don’t know that R0 for this new virus is, but estimates place it in the 1.5 to 2.5 range.  That means that if someone has 2019-ncov, they will, on average, transmit it to about 1.5, 2 or 2.5 other people.   That’s pretty infectious, but not nearly as bad as other viruses (Smallpox had a R0 of 3.5-6). 

But R0 is not all that matters when it comes to trying to limit or stop a virus from spreading.   One way to stop spread is through quarantine, but quarantines do not always work, and the best way to protect a population from a virus is for the population to have immunity to the virus.  A population can sometimes develop immunity by catching the virus (or a weaker version of it) through natural exposure, but the best way (at least in developed countries) to immunize a population is through immunization.   Which leads to the question of how many in the population need to be immunized to stop a virus from spreading?  This number of what percentage of a population needs immunization is called the “threshold.”

The answer depends on on how “effective” the vaccine is. The WHO states “no vaccine is 100% effective. To make vaccines safer than the disease, the bacteria or virus is killed or weakened (attenuated). For reasons related to the individual, not all vaccinated persons develop immunity. Most routine childhood vaccines are effective for 85% to 95% of recipients.” (see https://www.who.int/vaccine_safety/initiative/detection/immunization_misconceptions/en/index2.html )

Just as a stool has 3 legs, the answer to ‘how many need immunization’ (that is, the “Threshold”) has 3 variables:   R0 (how infectious), the Effectiveness of the Vaccine, and the Threshold number.

Imagine the extreme of a virus with very low R0 of 1.1 — it is barely infectious at all.  Therefore, if you have a highly effective vaccine, you don’t need the Threshold percentage of the population to be high.   But if the vaccine is relatively ineffective, then you need to inoculate a higher Threshold.

At the other extreme, if a virus has a very high R0 of 5 or 8, then you need both the vaccine to be quite effective, and you need to vaccinate a very high Threshold percentage of the population.

~~ Robert Carr