I think our immune system is cyclic. And your immune reaction depends on the phase of that cycle.
Everything cyclic, even the vibrations of atoms, so yes, I think you are correct in postulating the immune system is cyclic as well.
No one has looked to see if there are common frequencies one might perceive by studying immune function over time, over generations. My guess is there are.
Cyclic means more than just a single cycle. Think energy which we perceive as vibrations.
Cycles are complex. Everything, literally, is connected. At a bare minimum you would have regular, transverse waves interacting or superposing with longitudinal waves resulting in superficially apparent irregularity or chaos cloaking order.
Longitudinal wave impacts might be nutrition, starvation, deficiencies, toxins, parasites, microorganisms both commensal and averse, etc. Even sun cycles which trigger droughts would impact immune system cycles.
Energy flows where you focus your attention, so if you focus on robust health that too becomes a wave form that impacts any natural frequency of the immune system.