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Self-activation coupled to a transport mechanism results in traveling wavesthat describe polymerization reactions, forest fires, tumor growth, and eventhe spread of epidemics. Diffusion is a simple and commonly used model ofparticle transport. Many physical and biological systems are, however, betterdescribed by persistent random walks that switch between multiple states ofballistic motion. So far, traveling fronts in persistent random walk modelshave only been analyzed in special, simplified cases. Here, we formulate thegeneral model of reaction-transport processes in such systems and show how tocompute the expansion velocity for arbitrary number of states. For thetwo-state model, we obtain a closed-form expression for the velocity and reporthow it is affected by different transport and replication parameters. We alsoshow that nonzero death rates result in a discontinuous transition fromquiescence to propagation. We compare our results to a recent observation of adiscontinuous onset of propagation in microtubule asters and comment on theuniversal nature of the underlying mechanism.

Traveling fronts in self-replicating persistent random walks with multiple internal states