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.

The Wikipedia article is nice.