A stochastic SIR model on a random network with given vertex degrees

We consider a stochastic SIR model on a random network (graph). Infected individuals infect susceptible neighbours at a fixed rate, and recover at another fixed rate.

The network is a random graph with given vertex degrees; equivalently, it is constructed by the configuration model.

The evolution of the number of infected individuals as a function of time is studied. We show (under suitable conditions) that as the size of the population tends to infinity, the number of infected converges after normalization to a deterministic function, described by a system of ordinary differential equations (originally found, heuristically, by Volz (2008)).

The model allows for starting with a substantial fraction of the population already infected, or already recovered (immune); the latter option can be used to study the effect of different vaccination strategies.

Based on joint papers with Malwina Luczak, Peter Windridge and Thomas House.

Please report video problems to itsupport@slmath.org.

See more of our Streaming videos on our main VMath Videos page.