Is a 40% reduction in flu transmission enough?

The Intercept fund starts with some strong statements:

Respiratory viruses kill 1 million people a year, cost us $600B annually, disrupt everyday life, and periodically threaten civilization.

and has some ambitious goals to improve the quality of the air we breathe in while indoors, the indoor air quality (IAQ):

Our goal is to catalyze the uptake of air cleaning technologies that safely reduce infectious aerosols by >75% and have a path to >50% uptake in transmission-relevant indoor spaces at low cost.

This level of ambition is, I guess, to be expected from a charity funded by the charitable arms of Anthropic and OpenAI, currently building trillion-dollar data centres*.

Reducing the amount of infectious aerosols in the air by 75% is ambitious. Often the air quality of pubs, public transport, schools, etc is poor but improving it by a factor of 4 is still a tall order. But is it enough?

For airborne transmission if we split transmission into the fraction over short ranges f_SR and the fraction of longer range transmission f_LR, then

where R₀ is the number infected (on average) by one infected person, when the whole population is susceptible**, and f_SUS is the fraction of the population that is susceptible to infection.

As the short-range transmission is via someone inhaling an infected person’s breath more-or-less directly, it is essentially unaffected by filtering the air or increasing ventilation rates. But the indoor air quality (IAQ) does affect the fraction of longer-ranged transmission.

Increasing the air turnover rate likely has a sublinear affect on transmission, i.e., doubling ventilation does not half the amount of transmission, the reduction is less than that. Based on data from the NHS app many of us used during the pandemic (for COVID transmission) I estimate that the relationship is roughly that the transmission risk scales approximately as the square root of the exposure. This implies that after meeting the Intercept’s fund target of cleaning the air of 75% of infectious aerosols, the transmission is now

I am not sure anyone has anything other than guesses for the values of the fractions f_LR and f_SR = 1 − f_LR and they will depend on essentially everything: what the room is, who is in the room etc etc. But if I guess that transmission is 3/4 long range, then cleaning the air of 75% of infectious aerosols reduces transmission by a bit less than 40%.

If the basic reproduction number is 3, this implies that without air cleaning, then transmission occurs until the fraction susceptible drops to 1/3 = 30%. While with air cleaning, transmission stops when the fraction is 60%. Assuming that the fraction susceptible is just the fraction not yet infected***, this means that with air cleaning transmission stops when 40% have been already been infected. As opposed to only stopping when 70% have been infected.

This looks like a worthwhile drop in the number of people infected. It also, I think, illustrates the point that it looks very hard to eliminate airborne infectious diseases, but we can reduce the number of people they infect and make sick.

* Plus flulab, set up Dr Lucinda Southworth, the wife of Google’s Larry Page.

** This is perhaps a rather rough description of the basic reproduction number typically written as R₀ , eg see its Wikipedia page.

*** See this Wikipedia page for the standard SIR model from epidemiology which classifies people into Susceptible, Infected (and so infectious) and Recovered.