  his paper describes and analyzes the spatial spread of tuberculosis (TB) on
complex metapopulation, that is, networks of populations connected by migratory
flows whose configurations are described in terms of connectivity distribution
of nodes (patches) and the conditional probabilities of connections among
classes of nodes sharing the same degree. The migration and transmission
processes occur simultaneously. For uncorrelated networks under the assumption
of standard incidence transmission, we compute the disease-free equilibrium and
the basic reproduction number, and show that the disease-free equilibrium is
locally asymptotically stable. Moreover, for uncorrelated networks and under
assumption of simple mass action transmission, we give a necessary and
sufficient conditions for the instability of the disease-free equilibrium.
  The existence of endemic equilibria is also discussed. Finally, the
prevalence of the TB infection across the metapopulation as a function of the
path connectivity is studied using numerical simulations.
