  The possibility of spreading by migration, colonizing new spatial domains
suitable for development and reproduction, can substantially relieve a
biological population from the risk of extinction. By means of a realistic
computational model based on empirical data, we study this phenomenon for the
human head louse, Pediculus humanus capitis. In particular, we show that a lice
colony infesting a single isolated host is prone to extinction by stochastic
population fluctuations within an interval of several months, while migration
over a relatively small group of hosts in contact with each other is enough to
insure the prevalence of the infestation for indefinitely long periods. We
characterize the interplay of the size of the host group with the host-to-host
contagion probability, which controls a transition between extinction of the
lice population and a situation where the infestation is endemic.
