hypothetical spread of infection through complex social networks
DESCRIPTION
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/TRANSCRIPT
HYPOTHETICAL SPREAD OF INFECTION THROUGH COMPLEX SOCIAL NETWORKSDaniel Stokes, Tom Downes and Mathew Seymour
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
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
MODELS
Early models: The SIS model The SIR model.
Most commonly used is the SIR model Where the change in the number of S, I and R is
given by:
Where the probability of transition is:
THE SIR MODEL: INFECTION RATE
THE SIR MODEL: EPIDEMIC THRESHOLD
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
NETWORKED SIS MODEL
NETWORKED SIR MODEL
NEWMAN'S 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.
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
SIMULATIONS
Simulations use multiple models together Example: Episims
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