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# Hypothetical spread of infection through complex social networks

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Presentation of a project done by a group students of the "Science of Complex Systems 2012" course at University of Kent, UK.
http://blogs.kent.ac.uk/complex/lectures-ph724/

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### Hypothetical spread of infection through complex social networks

1. 1. HYPOTHETICAL SPREAD OFINFECTION THROUGH COMPLEXSOCIAL NETWORKSDaniel Stokes, Tom Downes and Mathew Seymour
2. 2. OUTLINE Introduction  Why model the spread of disease? Early Models  SIR / SIS theory and model Network Models  Lattice, Random and Scale Free Newman’s Adaptation Scale Free Networks Simulations Future Research / Conclusions
3. 3. INTRODUCTIONWHY MODEL THE SPREAD OF DISEASE Viral strains transmitted across the population by close proximity or contact We live in a highly connected world Determine risk Targeted Vaccination
4. 4. MODELS
5. 5. THE SIR MODEL: INFECTION RATE
6. 6. THE SIR MODEL: EPIDEMIC THRESHOLD
7. 7. NETWORK MODELS Adapted the SIS and SIR models to fit three different networks; a lattice, a random network, and a scale free network A lattice network is a regular grid of vertices In a random network, vertices are connected at random In a scale free network, the degree distribution of the vertices follows a power law The adapted models are stochastic, and designed to mimic the SIS and SIR models
8. 8. NETWORKED SIS MODEL
9. 9. NETWORKED SIR MODEL
10. 10. NEWMANS SIR ADAPTATION SIR models adapted to fit a random graph using the ideal Bond percolation to carry the infection. Use a power law degree distribution to model the network connections β. Produced models with an epidemic threshold corresponding to an exponent > 3. Problem is that some people are still connected to all others.
11. 11. CLUSTERING IN SCALE FREE NETWORKS Eguiluz and Klemm propose scale free networks do have an epidemic threshold! Real networks are more clustered than “random scale free networks” High clustering leads to low connectivity between connectivity between hubs BUT this is also unrealistic
12. 12. SIMULATIONS Simulations use multiple models together Example: Episims
13. 13. FUTURE RESEARCH New variables can be added to take into account more real world effects, for example: variable susceptibility, asymptomatic carriers and seasonality Can also adapt the types of network used, by making them dynamic, or perhaps introducing directed edges Combining these adaptions will improve the fit the model has with the real world