A two-phase epidemic driven by diffusion

In this paper, I present and analyse a model for the spatial dynamics of an epidemic following the point release of an infectious agent. Under conditions where the infectious agent disperses rapidly, relative to the dispersal rate of individuals, the resulting epidemic exhibits two distinct phases: a primary phase in which an epidemic wavefront propagates at constant speed and a secondary phase with a decelerating wavefront. The behavior of the primary phase is similar to standard results for diffusive epidemic models. The secondary phase may be attributed to the environmental persistence of the infectious agent near the release point. Analytic formulas are given for the invasion speeds and asymptotic infection levels. Qualitatively similar results appear to hold in an extended version of the model that incorporates virus shedding and dispersal of individuals.