Analysis of the spread of tuberculosis in heterogeneous complex metapopulations

This 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 diseasefree 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.