Avoiding extinction by migration. The case of the head louse

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.