This is a screenshot from the UK PM’s statement to the nation regarding a roadmap towards ending the current Coronavirus lockdown.
Taken literally the equation is clearly nonsense. As you’ll know, the value of R is somewhere around 1: values slightly smaller than 1 imply the epidemic is decaying, values greater than 1 imply it is growing exponentially. But, even the most pessimistic estimates of R before the lockdown were around 5. On the other hand, the number of current infections is in the several thousands, with large fluctuations from day to day. So, the inclusion of R in this equation is virtually irrelevant, and the Alert Level would oscillate wildly from day to day with the number of infected individuals.
Let’s assume instead that it’s intended that the number of infections is scaled – say by 1000. So, if R is 1 and the number of infections is 2,500, then the Alert Level would be 3.5. But still it doesn’t make much sense. Suppose you managed to eradicate transmission, so that R=0, but you still had 3000 infected in the population. Then the Alert Level would be 3, even though there would be no risk of further infection. Moreover, would an increase of 1 in the value of R be equally serious as an increase of 1000 in the number of infected individuals, as the equation implies? Generally, that would depend on the actual number of infected individuals: having 20,000 rather than 19,000 infected probably won’t alter the course of the epidemic very much, but having R=1.5 rather than R=0.5 most definitely would.
So, any literal interpretation of the slide, even allowing for scaling effects, is completely false. What is presumably intended is that decisions take on determining an Alert Level will be driven by two factors: the current estimated rate of transmission and the current number of infected individuals. By far the most important of these is the rate of transmission, since the nature of exponential growth is that just a few cases will become many thousands in a short period of time if R is bigger than 1. But the number of cases is relevant. Partly because it affects the number of new infected, especially in the short term; but more so because, if the number is sufficiently low, then a policy of containment through testing and contact tracing is feasible.
In summary: if you disregard any literal interpretation of the equation, but regard it as saying that two primary factors need to be considered when determining an appropriate Alert Level for COVID, then it makes some sort of sense. But presenting complex arguments in a way that makes them seem simpler is both patronising and counter-productive.