Probability seminar: Extinction time for the weaker of two competing SIS epidemics

Cancelled

3 June 2016, 3.40 PM - 3 June 2016, 4.40 PM

Malwina Luczak, Queen Mary, University of London

SM3, School of Mathematics

Malwina Luczak, Queen Mary, University of London

Extinction time for the weaker of two competing SIS epidemics

We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. In our model, the spread of each strain is described by the stochastic logistic SIS epidemic process in the absence of the other strain, and we assume that there is perfect cross-immunity between the two virus strains, that is, individuals infected by one strain are temporarily immune to re-infections and infections by the other strain. For the case where one strain has a strictly larger basic reproductive ratio than the other, and the stronger strain on its own is supercritical (that is, its basic reproductive ratio is larger than 1), we derive precise asymptotic results for the distribution of the time when the weaker strain disappears from the population, that is, its extinction time. We further extend our results to the case where the difference between the two reproductive ratios may tend to 0.

In our proof, we set out a simple approach for establishing a fluid limit approximation for a sequence of Markov chains in the vicinity of a stable fixed point of the limit drift equations, valid for a time exponential in the system size.

Contact information

Organisers: Marton Balazs, Haeran Cho

Edit this page