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Extinction time for the weaker of two competing SIS epidemics

Presented by: 
Malwina Luczak Queen Mary University of London
Date: 
Thursday 8th September 2016 - 14:00 to 15:00
Venue: 
INI Seminar Room 2
Abstract: 
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 consider what happens when the difference between the two reproductive ratios may tend to 0.

In our proof, we set out an approach for establishing a long-term fluid limit approximation for a sequence of Markov chains in the vicinity of a stable fixed point of the limit drift equations.
  This is joint work with Fabio Lopes.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons