Abstract
The basic contact process with parameter μ altered so that infections of sites that have not been previously infected occur at rate proportional to λ instead is considered. Emergence of an infinite epidemic starting out from a single infected site is not possible for μ less than the contact process’ critical value, whereas it is possible for μ greater than that value. In the former case the space and time infected regions are shown to decay exponentially; in the latter case and for λ greater than μ, the ratio of the endmost infected site’s velocity to that of the contact process is shown to be at most λ/μ.
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