myxomatosis is a lethal disease for the european rabbit (oryctolagus cuniculus) produced by the myxoma virus and transmitted by mosquitos and fleas. myxomatosis has been used for the biological control of exotic populations of the european rabbit in some countries, for example in australia. exotic rabbit populations produce an important negative impact on the economy of diverse regions of the world, including argentina. in this work we present mathematical models representing the local dynamics of myxomatosis as well as its dispersion on wild populations of o. cuniculus, the latter with the aid of an explicit spatial model. the dispersion speeds obtained are consistent with those obtained in field studies in great britain, but under-estimate observations made in australia. resorting to stochastic simulations we show that the likelihood for myxomatosis to be established depends on the viral strain used. the standard strategy, consisting in introducing highly virulent strains in wild rabbits populations, might not be the optimal according to our results.