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SUMMARY:Extinction time for the weaker of two competing SIS epidemics - Ma
 lwina Luczak (Queen Mary University of London)
DTSTART:20160908T130000Z
DTEND:20160908T140000Z
UID:TALK67284@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>We consider a simple stochastic model for the spread of 
 a disease caused by two virus strains in a closed homogeneously mixing pop
 ulation of size N. In our model\, the spread of each strain is described b
 y the stochastic logistic SIS epidemic process in the absence of the other
  strain\, and we assume that there is perfect cross-immunity between the t
 wo virus strains\, that is\, individuals infected by one strain are tempor
 arily 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 asympt
 otic results for the distribution of the time when the weaker strain disap
 pears from the population\, that is\, its extinction time. We further cons
 ider what happens when the difference between the two reproductive ratios 
 may tend to 0.<br> <br> In our proof\, we set out an approach for establis
 hing a long-term&nbsp\;fluid limit approximation for a sequence of Markov 
 chains in the vicinity of a stable fixed point of the limit drift equation
 s.</span>  &nbsp\;  This is joint work with Fabio Lopes.
LOCATION:Seminar Room 2\, Newton Institute
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