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Table of contents
1 Preface
2 Background & definitions
2.1 Why do we use models ?
2.2 The SIR model
2.2.1 Transmission rate
2.2.2 Recovery rate
2.2.3 Basic reproduction ratio
2.2.4 Extensions of the SIR model
2.3 Spatial models
2.3.1 Patch models
2.3.2 Distance transmission
2.3.3 Network models
3 Disease propagation in the light of human mobility
3.1 Article
3.2 Observations
4 Influence of commuting movements on influenza propagation
4.1 Introduction
4.2 Spatial autocorrelation of influenza incidence
4.2.1 Investigating the link between influenza propagation and commuting: spatial autocorrelation and model design
4.2.2 Observations and Perspectives
4.3 Influence of the network structure on the propagation
4.3.1 Relation between the structure of commuting networks and similarities between epidemic courses
4.3.2 Article
4.3.3 Observations, Supplementary informations and Perspectives
4.3.4 Structure of the network and similarities between epidemic propagation
4.3.5 Interpretation and perspectives
4.4 Conclusion
5 Districts role in the system dynamics
5.1 Linearized model
5.1.1 Linearization
5.2 Kernels
5.2.1 Kernel definition
5.2.2 Kernel analysis
5.3 Perspectives of use for the kernels
5.4 Conclusion
6 Analysis of the system global dynamics
6.1 Next generation operator
6.2 Eigenvalues and eigenvectors of the next generation operator
6.2.1 Isolated districts
6.2.2 Partial analyses for isolated areas
6.2.3 Perspectives
6.3 Conclusion
7 Technical development
7.1 Management of the simulations
7.1.1 OpenMOLE and simulations on grid
7.1.2 From stochastic to deterministic
7.2 Management of the results
8 Conclusion
8.1 Influence of commuting structure on influenza propagation .
8.1.1 Role of commuting in the propagation
8.1.2 Age related commuting
8.1.3 Underlying structure: attractors and basins of attraction
8.2 New methodology for network analysis
8.2.1 Early propagation
8.2.2 Global dynamics
