These requirements are too strict. The main requirement is that average reproduction rate stays reasonably well below 1. If it fluctuates between 0.1 and 0.9

These requirements are too strict. The main requirement is that average reproduction rate stays reasonably well below 1. If it fluctuates between 0.1 and 0.9 in time or between people, you still have heard immunity. Presumably, Interesting things happen around 1.0, where the instability can push you either way. Hence heard immunity is almost a binary state.