A tractable deterministic model with realistic latent period for an epidemic in a linear habitat

This paper describes a model for the spatial spread of an epidemic in which the latent period has a Gamma distribution with arbitrary mean and variance while the infected and uninfected may have different diffusion coefficients. Using a variant of the "linear chain trick" we derive a simple algorithm for the propagation speed of the infection front. By way of verification, we show that, with suitably matched parameters, the algorithm agrees closely with speeds obtained numerically from the corresponding model in which the latent period is a constant.