1. K. Peters, L. Buzna, and D. Helbing, 2008
Modelling of cascading effects and efficient response to disaster spreading in complex networks
K. Peters, L. Buzna, and D. Helbing, 2008
Alexandre Mérillat Nhat Anh Truong

2. Blackout of August 14, 2003
((Vorname Nachname))

3. Introduction
We are surrounded by networks: infrastructure, organisations, communication systems
To model complex systems:
System components = nodes
Relation between components = links (physical but also logical)
Understanding dynamics of failure spreading in complex networks:
Topology of underlying network
Dynamic mechanisms of interaction
Alexandre Mérillat Nath Anh Truong

4. Modelling the dynamics of disaster spreading

5. Network and node model (1)
Use a generic model: equation for behaviour of one system component that depends on internal & external loads
Sigmoid function of expected damage (specific fragility curve)
θi : threshold (node fails if sum of all disturbances approach θi)
Alexandre Mérillat Nath Anh Truong

6. Network and node model (2)
We add interactions between components and the recovery ability of the component which tend to restore xi to zero.
Overal dynamic of node in an interaction network (with permanent recovery capabilities:
Alexandre Mérillat Nath Anh Truong

7. Dynamics of disaster spreading (1)
One initial extreme event
Three basic types of system behaviours are found:
1. self-healing scenario: damage grow and spread as long as disturbance persist, then go back
2. spreading scenario: damage grow even after disturbance ceased
3. intermediate regime
Which regime depends on recovery rate
Alexandre Mérillat Nath Anh Truong

8. Dynamics of disaster spreading (2)
1/τ decreases
Repair effect reduced
Alexandre Mérillat Nath Anh Truong

9. Dynamics of disaster spreading (3)
Fast propag.
Nonlinear dep.
Slower propag heterogeneous
Alexandre Mérillat Nath Anh Truong

10. Assessment of disaster management strategies

11. The strategies Uniform distribution of available forces
Out-degree based assignment of forces
Uniform assignment to damaged nodes
Uniform assignment to destroyed nodes
Targeted assignment to highly connected nodes
Out-degree-based targeted assignment to destroyed nodes
Alexandre Mérillat Nath Anh Truong

12. Modelling of resources allocation and damage mitigation
Alexandre Mérillat Nath Anh Truong

13. Efficiency of strategies (1)
Number of destroyed nodes for different strategies : solid line – strategy S3;
long-dashed line – S4; short-dashed line – S5; dotted line – S6
Alexandre Mérillat Nath Anh Truong

14. Efficiency of strategies (2)
Damages for two differences, an efficient (S6) and an inefficient one (S1), as a function of ressources R available and time delay for response tD
Alexandre Mérillat Nath Anh Truong

15. Conclusion
For real cases where resources are limited and reaction is within a time delay, choosing the strategy wisely can greatly improve the efficiency of the response. However, the good use of the strategy might be limited by a lack of information.
This model can help to optimise the robustness of existing networks and better prepare our response to disasters.
Alexandre Mérillat Nath Anh Truong

16. Thank you for your attention !
Questions ?
Thank you for your attention !