Terrific and clear answer Ken.
I had this naïve idea that I took to the bank about 40 years ago that cycles are typically explained by (a) celestial rotations (b) some kind of negative feedback. The example I studied in detail was the prey-predator model.
In the present case, the cycle is driven by a different dynamic but is still a kind of prey-predator model. The predator is the immune system and the prey is the virus. The prey changes occasionally, randomly and suddenly and the predator adapts but with a lag.
I guess the other natural way to think of the cyclic graph is as a superposition of several single wave infections of a sequence of different but related diseases.
Thanks so much.