01-23-2021, 01:16 PM

A fixed percentage increase in CFR (case fatality rate) or IFR (infection fatality rate) is important, but more important is R, at least under our current situation.

If one thinks that we will have a vaccine that can get to herd immunity by a particular date (Dh), then the number that will die is proportional to the number infected by that date. IFR*I(Dh).

The number infected is bound by the total population. If everyone will eventually get the disease, then, with either 0 or infinite medical resources, it doesn't matter how fast they get it. But, we are still under the impression that we can keep the total infected to be less than the total population. Further, we only have limited medical resources and IFR goes up when the number of currently infected is higher than our medical capacity.

IFR should be considered a function of current infections. IFR(0) is the fatality rate with full medical care. IFR(1billion) will be essentially IFR with no medical care. If CI(t) is current infections at time t, I(t) is total infections at time t (so I(Dh) = Integral over t of I(t) for now <= t <= Dh),

deaths = Integral over time t of IFR(CI(t)) for now <= t <= Dh.

R is a measure of how many new infections are caused by the current set of infections. If you take the current number of infections now, the number of infections one generation later is I(now + 1 generation) = R * I(now). For COVID-19, 1 generation is about 1 week (some say 5 or 6 days). If the number of infections are increasing, R is > 1. If they are decreasing, R<1. (R also depends on the number of susceptible individuals.)

An increase of say 10% in R will increase the number newly infected by 33% in 3 weeks, by 61% in 5 weeks, by 985% in 6 months. This impacts both I(Dh) and IFR(CI(t)) for t < Dh.

But, society (individually and by government) is reacting to the infection levels and mortality. The rate of spread ® is roughly controlled by shutting things down and by interventions such as mask wearing. So, if society perceives the disease as deadly, it responds by tolerating tighter controls, reducing R. Perception is a squishy concept. Things like public advice, news reports, and acceptance impact perception and the resultant behaviors. Perception is also impacted by the (sometimes false) belief that certain behaviors are more important than causing a few more people to be sick.

Society tried hard shutdowns early in the history of the disease: In China in January and in the US and elsewhere in March. COVID-19 has the unusual aspect of being infectious before symptoms which allowed it to escape those shutdowns.

Last night, in a televised basketball game, I watched a coach talk (without a mask) to her unmasked players from within 1 foot of their faces. She exposed them to any virus she might be shedding, and herself to any virus they might be shedding. She could have and, by state rules, was required to be wearing her mask. If she and/or her players get sick, she'll probably consider that to be bad luck, rather than stupidity and a lack of hygiene. I'd love to challenge her on that action today while it is uncertain whether people will get sick through her actions. In my opinion, I'd likely hear a reaction similar to someone who drove drunk last night, "Well, I didn't kill anyone," to which I'd add "Yet".

If one thinks that we will have a vaccine that can get to herd immunity by a particular date (Dh), then the number that will die is proportional to the number infected by that date. IFR*I(Dh).

The number infected is bound by the total population. If everyone will eventually get the disease, then, with either 0 or infinite medical resources, it doesn't matter how fast they get it. But, we are still under the impression that we can keep the total infected to be less than the total population. Further, we only have limited medical resources and IFR goes up when the number of currently infected is higher than our medical capacity.

IFR should be considered a function of current infections. IFR(0) is the fatality rate with full medical care. IFR(1billion) will be essentially IFR with no medical care. If CI(t) is current infections at time t, I(t) is total infections at time t (so I(Dh) = Integral over t of I(t) for now <= t <= Dh),

deaths = Integral over time t of IFR(CI(t)) for now <= t <= Dh.

R is a measure of how many new infections are caused by the current set of infections. If you take the current number of infections now, the number of infections one generation later is I(now + 1 generation) = R * I(now). For COVID-19, 1 generation is about 1 week (some say 5 or 6 days). If the number of infections are increasing, R is > 1. If they are decreasing, R<1. (R also depends on the number of susceptible individuals.)

An increase of say 10% in R will increase the number newly infected by 33% in 3 weeks, by 61% in 5 weeks, by 985% in 6 months. This impacts both I(Dh) and IFR(CI(t)) for t < Dh.

But, society (individually and by government) is reacting to the infection levels and mortality. The rate of spread ® is roughly controlled by shutting things down and by interventions such as mask wearing. So, if society perceives the disease as deadly, it responds by tolerating tighter controls, reducing R. Perception is a squishy concept. Things like public advice, news reports, and acceptance impact perception and the resultant behaviors. Perception is also impacted by the (sometimes false) belief that certain behaviors are more important than causing a few more people to be sick.

Society tried hard shutdowns early in the history of the disease: In China in January and in the US and elsewhere in March. COVID-19 has the unusual aspect of being infectious before symptoms which allowed it to escape those shutdowns.

Last night, in a televised basketball game, I watched a coach talk (without a mask) to her unmasked players from within 1 foot of their faces. She exposed them to any virus she might be shedding, and herself to any virus they might be shedding. She could have and, by state rules, was required to be wearing her mask. If she and/or her players get sick, she'll probably consider that to be bad luck, rather than stupidity and a lack of hygiene. I'd love to challenge her on that action today while it is uncertain whether people will get sick through her actions. In my opinion, I'd likely hear a reaction similar to someone who drove drunk last night, "Well, I didn't kill anyone," to which I'd add "Yet".