Dynamics of the spread of tuberculosis in heterogeneous complex metapopulations. (English) Zbl 1275.34066
Summary: This paper analyzes the dynamics of the 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, we give a necessary and sufficient condition 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.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34F05 | Ordinary differential equations and systems with randomness |
| 92C60 | Medical epidemiology |
| 92C42 | Systems biology, networks |
Keywords:
dynamical systems; tuberculosis; complex metapopulation; uncorrelated networks; basic reproduction number; stabilityReferences:
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