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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Extinction time for the weaker of two competing SI
 S epidemics - Malwina Luczak (Queen Mary Universit
 y of London)
DTSTART;TZID=Europe/London:20160908T140000
DTEND;TZID=Europe/London:20160908T150000
UID:TALK67284AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/67284
DESCRIPTION:<span>We consider a simple stochastic model for th
 e spread of a disease caused by two virus strains 
 in a closed homogeneously mixing population of siz
 e N. In our model\, the spread of each strain is d
 escribed by the stochastic logistic SIS epidemic p
 rocess in the absence of the other strain\, and we
  assume that there is perfect cross-immunity betwe
 en the two virus strains\, that is\, individuals i
 nfected by one strain are temporarily immune to re
 -infections and infections by the other strain. Fo
 r 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 d
 istribution of the time when the weaker strain dis
 appears from the population\, that is\, its extinc
 tion time. We further consider what happens when t
 he difference between the two reproductive ratios 
 may tend to 0.<br> <br> In our proof\, we set out 
 an approach for establishing a long-term&nbsp\;flu
 id limit approximation for a sequence of Markov ch
 ains in the vicinity of a stable fixed point of th
 e limit drift equations.</span>  &nbsp\;  This is 
 joint work with Fabio Lopes.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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