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Adaptive immune systems engage in an arms race with evolving viruses, trying to generate new responses to viral strains that continually move away from the set of genetically varying strains that have already elicited a functional immune response. It has been argued that this dynamical process can lead to a propagating pulse of an ever-changing viral population and concomitant immune response. Here, we introduce a new stochastic model of viral-host coevolution, taking into account finite-sized host populations and varying processes of immune “forgetting”. Using both stochastic and deterministic calculations, we show that there is indeed a possible pulse solution, but for a large host population size and for finite memory capacity, the pulse becomes unstable to the generation of new infections in its wake. This instability leads to an extended endemic infection pattern, demonstrating that the population-level behavior of virus infections can exhibit a wider range of behavior than had been previously realized. Published by the American Physical Society2024 

Regulatory networks as large and complex as those implicated in cell-fate choice are expected to exhibit intricate, very high-dimensional dynamics. Cell-fate choice, however, is a macroscopically simple process. Additionally, regulatory network models are almost always incomplete and/or inexact, and do not incorporate all the regulators and interactions that may be involved in cell-fate regulation. In spite of these issues, regulatory network models have proven to be incredibly effective tools for understanding cell-fate choice across contexts and for making useful predictions. Here, we show that minimal frustration—a feature of biological networks across contexts but not of random networks—can compel simple, low-dimensional steady-state behavior even in large and complex networks. Moreover, the steady-state behavior of minimally frustrated networks can be recapitulated by simpler networks such as those lacking many of the nodes and edges and those that treat multiple regulators as one. The present study provides a theoretical explanation for the success of network models in biology and for the challenges in network inference.