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The adaptive immune system engages in an arms race with evolving viruses,trying to generate new responses to viral strains that continually move awayfrom the set of variants that have already elicited a functional immuneresponse. In previous work, it has been argued that this dynamical process canlead to a propagating pulse of ever-changing viral population and concomitantimmune response. Here, we introduce a new stochastic model of viral-hostcoevolution and a deterministic approximation thereof with which to study thesedynamics. We show that there is indeed a possible pulse solution, but for alarge host population size, the pulse becomes unstable to the generation of newinfections in its wake, leading to an extended endemic infection pattern. Thistime-dependent endemic pattern eventually reaches a fluctuating steady-statewhen the infected population size reaches a large enough fraction of the totalnumber of hosts.

Multiple possible patterns can emerge from virus-immune coevolution