Convergence rates for the one-dimensional three state contact process

Details Convergence rates for the one-dimensional three state contact process Convergence rates for the one-dimensional three state contact process

2011-02-14

arxiv.org/abs/1102.2810v1

Mathematics

Probability

Scientific paper

The nearest neighbours contact process with infection rate mu altered so that each initial infection occurs at rate lambda instead is considered. If there is a positive probability that the epidemic starting from a single infected site lasts forever the process is said to survive, while otherwise it is said to die out. Irrespectively of the value of lambda, for all mu throughout the contact process's subcritical phase the process dies out, while for all mu throughout its supercritical phase the process survives. In the former case we obtain certain exponential decay results; in the latter case, assuming additionally that mu > lambda, we prove that the ratio of the limit of the speed to that of the unaltered contact process is not greater than lambda over mu.

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