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