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Mathematical Biology Seminar
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
2019/06/20
16:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Eric Foxall (University of Alberta)
Diffusion limit for the partner model at the critical value (ENGLISH)
Eric Foxall (University of Alberta)
Diffusion limit for the partner model at the critical value (ENGLISH)
[ Abstract ]
The partner model is a stochastic SIS model of infection spread over a dynamic network of monogamous partnerships. In previous work, Edwards, Foxall and van den Driessche identify a threshold in parameter space for spread of the infection and show the time to extinction of the infection is of order log(N) below the threshold, where N is population size, and grows exponentially in N above the
threshold. Later, Foxall shows the time to extinction at threshold is of order sqrt(N). Here we go further and derive a single-variable diffusion limit for the number of infectious individuals rescaled by sqrt(N) in both population and time, and show convergence in distribution of the rescaled extinction time. Since the model has effectively four variables and two relevant time scales, the proof features a succession of probability estimates to control trajectories, as well as an averaging result to contend with the fast partnership dynamics.
The partner model is a stochastic SIS model of infection spread over a dynamic network of monogamous partnerships. In previous work, Edwards, Foxall and van den Driessche identify a threshold in parameter space for spread of the infection and show the time to extinction of the infection is of order log(N) below the threshold, where N is population size, and grows exponentially in N above the
threshold. Later, Foxall shows the time to extinction at threshold is of order sqrt(N). Here we go further and derive a single-variable diffusion limit for the number of infectious individuals rescaled by sqrt(N) in both population and time, and show convergence in distribution of the rescaled extinction time. Since the model has effectively four variables and two relevant time scales, the proof features a succession of probability estimates to control trajectories, as well as an averaging result to contend with the fast partnership dynamics.
