  Recently, many empirical studies uncovered that animal foraging, migration
and human traveling obey Levy flights with an exponent around -2. Inspired by
the deluge of H1N1 this year, in this paper, the effects of Levy flights'
mobility pattern on epidemic spreading is studied from a network perspective.
We construct a spatial weighted network which possesses Levy flight spatial
property under a restriction of total energy. The energy restriction is
represented by the limitation of total travel distance within a certain time
period of an individual. We find that the exponent -2 is the epidemic threshold
of SIS spreading dynamics. Moreover, at the threshold the speed of epidemics
spreading is highest. The results are helpful for the understanding of the
effect of mobility pattern on epidemic spreading.
