There's quite a bit more to COVID-19 prediction than standard derivation of a logistic curve found in introductory differential equation books. SIR models would perhaps be the simplest place to start.
Nice reference. The discussion is mostly about SIR (for susceptible, infected and recovered) models but also with several generalizations to handle more details, e.g., losing immunity and getting infected again. A lot of this material goes back, say, to 1927.
First cut it appears that the differential equation I gave is an SIR model except with R = 0, i.e., once are a customer of FedEx then remain one.
At one point article finds the logistic curve as I did -- maybe for the same situation.
The article does touch on stochastic models, but I didn't see discussion of a Markov assumption or Poisson process for time to the next infection.
There is an unclear reference to operator spectral radius, and maybe that is related to the eigenvalues, vectors I mentioned.
Whatever, especially with the Wikipedia reference, it appears that we are a step or two beyond the OP.
The work I did and described here I did decades ago and is not at all related to the math of my startup now. So, here I was able to describe some of my old work, but I'm doing other things now.
For the differential equation I gave, the solution as I derived it needed only ordinary calculus and not the additional techniques of differential equations. I just did the derivation in a hurry at FedEx just as a little calculus exercise. I didn't consult a differential equations book. I discovered that the solution was the logistic curve only by accident years later.
Yes that's I nice way to run into logistic. Some introductory books use that as a motivating example, usually the second one. SIR is too simple to be accurate, but is ok enough to paint with broad brush strokes. Sometimes simple models are still useful as long as one does not read too much into the output.
Statistical epidemiology is quite heavily invested in stochastic differential equation. Wikipedia would hardly suffice as an academic, up to date and an exhaustive bibliography.
BTW you mention Prof. Bertsekas a few times, did you ever run into Pof. Tsitsiklis ? He has done some work in the area of epidemics around 2015. Mentioning just in case you knw him
Perhaps the optimal control problem would pique your interest more, once the differential equations have been nailed down in a form that also incorporates the interventions.
https://en.wikipedia.org/wiki/Compartmental_models_in_epidem...