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Machine Learning of Epidemic Processes in Networks
- 1. Machine Learning of Epidemic Processes in Networks Francisco Rodrigues Institute of Mathematics and Computer Science University of São Paulo francisco@icmc.usp.br Workshop on Modelling of Infectious Diseases Dynamics
- 2. Outline 1. Complex Networks 2. Epidemic processes in networks 3. The influence of network structure 4. Prediction of epidemic processes 5. Challenges and future research
- 4. What is a network? John Tom Mary Ann 1 2 3 4 Graph Nodes EdgesFriendship
- 7. Example: Internet Internet Nodes: Autonomous systems, routers Links: Physical connections
- 9. Network Science is a well stablished area.
- 10. To describe the network topology, we need networks measures. x = [x1, x2,…]
- 11. Adjacency matrix
- 12. Degree
- 14. Paul Anne Society: Six degrees S. Milgram 1967 WWW: 19 degrees Albert et al. 1999 Distance = 3 Distance Mike Jane
- 16. • Spectra • Entropy based-measures • Centrality • Subgraphs • ... Costa, Rodrigues,Travieso,Villas Boas.Advances in Physics 2007 Network measures
- 17. Structure Dynamics Applications Complex Networks
- 18. • Resilience • Epidemic spreading, • Rumor spreading, • Random walks, • Synchronization, • Transport, • Cooperation and competition, …. Dynamic processes in networks
- 20. How does the network structure influence epidemic spreading?
- 21. Bubonic Plague
- 23. Spreading depends on the network structure! Can we quantity this dependence?
- 24. Susceptible (healthy) Infected (sick) Removed (immune / dead) S I R Infection Recovery Recovery Removal Epidemic models
- 25. Pastor-Satorras et al. Reviews of Modern Physics 2014 Epidemic models
- 26. Degree-based mean field: SIS model v Keeping only the first order terms: Multiplying the equation with (k–1)pk/〈k〉 and summing over k characteristic time the fraction of infected neighbors of a susceptible node k Epidemic models in networks
- 27. Degree-based mean field: SIS model A global outbreak is possible if τ>0, which yields the condition for a global outbreak as Satorras andVespignani, PRL, 2001 Epidemic models in networks
- 28. A. L. Barabási, Network Science, Cambridge, 2015. 0~ Epidemic models in networks
- 29. Epidemic spreading with awareness Rumour spreading Disease transmission
- 31. Epidemic spreading with awareness Ignorant Spreader Stifler Ignorant Suceptible Infected Suceptible Layer 1 Layer 2 Rumour Disease
- 32. Epidemic spreading with awareness Ventura da Silva et al., Phys. Rev. E 100, 2019 • The rumour and disease propagate with different velocities. • At each time step: π : information 1 − π : disease
- 35. Epidemic spreading with awareness • If the rumor propagation is too fast, the outbreak increases! Ventura da Silva et al., Phys. Rev. E 100, 2019
- 36. Epidemic spreading with awareness Applications • Infectious diseases with no symptoms (Sexually transmitted diseases (STD)).
- 37. Spreading depends on the network structure! Arruda, Rodrigues and Moreno, Physics Reports, 2018
- 38. Epidemic spreading depends on the network structure. Can we predict this dynamical processes?
- 39. = f( ) + E Hypothesis: Yi =f(Xi)+εi f(x) : ℝd → ℝ d: number of features Structure X Dynamics: Prediction
- 40. Yi =f(Xi)+εi • The function f is very complicated due to the presence of non-trivial patterns of connections, nonlinear effects and correlations between variables… f(x) : ℝd → ℝ Structure X Dynamics: Prediction Rodrigues et al., https://arxiv.org/abs/1910.00544
- 41. Yi =f(Xi)+εi Solution: Machine Learning Structure X Dynamics: Prediction Rodrigues et al., https://arxiv.org/abs/1910.00544
- 42. Data X Y k(i), cc(i), B(i), PR(i), kc(i), ec(i) … k(j), cc(i), B(i), PR(i), kc(i), ec(i) … node i yi … yj …
- 43. Dynamical processes • Epidemic spreading: we defi neYi as the expected fraction of infected nodes when the disease starts in i Regression Rodrigues et al., https://arxiv.org/abs/1910.00544
- 44. Machine learning: • To obtain the function • Random forests • Neural Networks f(x) : ℝd → ℝ Rodrigues et al., https://arxiv.org/abs/1910.00544
- 46. Random forests
- 47. Predictive learning Training set k(1), cc(1), …, kc(1), ec(1) … k(l), cc(l), …, kc(l), ec(l) k(l+1), cc(l+1), …, kc(l+1), ec(l+1) … k(N), cc(N), …, kc(N), ec(N) Testing set Rodrigues et al., https://arxiv.org/abs/1910.00544
- 48. Epidemic spreading US air transportation network Hamsterster social network (social network for hamsters)
- 49. Identification of influential spreaders
- 52. Can we identify the most “important” nodes from the network structure?
- 53. γ = 2.5 γ = 2.1 γ = 2. 5 Newman, Siam, 2003 Networks are heterogeneous
- 56. Centrality X Epidemic Spreading Can we improve this correlation?
- 57. Random walk accessibility measure
- 58. Centrality X Epidemic Spreading
- 59. Centrality X Epidemic Spreading Japan England US Germany Arruda et al., PRE, 2014
- 60. Sperman correlation coefficient Centrality X Epidemic Spreading Arruda, Barbieri, Costa, Rodriguez, Moreno, Rodrigues, PRE, 2014
- 61. What measure is the most suitable to predict epidemic spreading? Degree, betweenness centrality, closeness centrality, PageRank, …?
- 62. = f( ) + E Hypothesis: Yi =f(Xi)+εi f(x) : ℝd → ℝ d: number of features Structure X Dynamics: Prediction
- 63. Random forests
- 64. There is no single measure we can use for the identification of the most influential spreaders! What measure is the most suitable to predict disease spreading?
- 65. A combination of measures is more suitable for the identification of the most influential spreaders. What measure is the most suitable to predict disease spreading?
- 66. Machine learning is a very useful tool to predict dynamical processes from the network structure.
- 67. Challenges • How to predict disease propagation from the networks structure. • The modeling of temporal interactions and multilayer organization. • Host heterogeneities. • Methods for control: quarantine, vaccination. • Identification of influential spreaders.