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A reaction-diffusion model is investigated to understand infectiveenvironments in a man-environment-man epidemic model.  The free boundary is introduced to describe the expanding front of aninfective environment induced by fecally-orally transmitted disease. The basicreproduction number $R^F_0(t)$ for the free boundary problem is introduced, andthe behavior of positive solutions to the reaction-diffusion system isdiscussed. Sufficient conditions for the bacteria to vanish or spread aregiven. We show that, if $R_0\leq 1$, the bacteria always vanish, and if$R^F_0(t_0)\geq 1$ for some $t_0\geq 0$, the bacteria must spread, while if$R^F_0(0)<1<R_0$, the spreading or vanishing of the bacteria depends on theinitial number of bacteria, the length of the initial habitat, the diffusionrate, and other factors. Moreover, some sharp criteria are given.

The spreading fronts of an infective environment in a man-environment-man epidemic model