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Standard Reaction-Diffusion (RD) systems are characterized by infinitevelocities and no persistence in the movement of individuals, two conditionsthat are violated when considering living organisms. Here we consider adiscrete particle model in which individuals move following a persistent randomwalk with finite speed and grow with logistic dynamics. We show that when thenumber of individuals is very large, the individual-based model is welldescribed by the continuous Reactive Cattaneo Equation (RCE), but for smallervalues of the carrying capacity important finite-population effects arise. Theeffects of fluctuations on the propagation speed are investigated bothconsidering the RCE with a cutoff in the reaction term and by means ofnumerical simulations of the individual-based model. Finally, a more generalL\'evy walk process for the transport of individuals is examined and anexpression for the front speed of the resulting traveling wave is proposed.

Reaction fronts in persistent random walks with demographic stochasticity