Why be surprised? It's just a bunch of simple differential equations.

SIR is for diseases with lifelong immunity, that's why it's used to design vaccination programs (re improving policies).

Intrigued, not surprised. Since, in the basic model , the quantity I (the #infected) multiplies each term, the epidemic equilibrium

has that equal to zero but the others variables are in some sense degenerate/undetermined.

However, clearly an equilibrium solution exists, but to get it you have to solve the dynamics, rather than searching for equilibrium points.

The T->infty levels for S and R are the solutions of those transcendental equations, (that I was looking for an approx for, to see how many of us are going to drop dead of this thing, at least in one version of the theory!)

Solutions that involve transforming a system of ODEs to get to a Bernoulli or Riccati equation, (like this one), I always find a bit magical.

They cropped up for me years back in mechanics. If you make any minor sounding changes in the system (e.g. time dependent parameter)

the whole solution technique falls apart, which makes me wonder what is "special" about this configuration.

I actually wrote a microsimulation model of an Internet worm spreading in a computer network to evaluate the cybersecurity threat and design prevention strategies... But now I have to go back to my craft beer

Somehow craft beer always reminds me of Aubrey de Grey's method to live forever!