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SUMMARY:A novel discrete-time model with waning immunity   - Desmond Lai\,
  University of Cambridge
DTSTART:20230308T120000Z
DTEND:20230308T130000Z
UID:TALK197965@talks.cam.ac.uk
CONTACT:Paula Smith
DESCRIPTION:Diseases with waning immunity cause people with prior immunity
  (previous infection or vaccination) to be susceptible to infection again.
  This was evidenced in COVID-19. We formulate a model at the population le
 vel to understand how the number of new infections changes in the long run
  in a closed population.  \n\nIn the same spirit as Kermack and McKendrick
  (1927\, 1932 and 1933)\, we make use of two key features in our model: (i
 ) time since infection and (ii) time since start of recovery. The former a
 llows us to keep track of how the infectiousness of an infected individual
  changes with time\, while the latter enables protection due to prior immu
 nity to be included.  \n\nWe perform stability and bifurcation analyses to
  obtain explicit conditions for which a disease goes extinct\, stays at th
 e endemic equilibrium\, or causes an oscillatory number of new infections.
  The last regime (oscillatory solution) is a long-term dynamic that is not
  observed in the simple continuous-time geometric (exponential) distributi
 on Susceptible-Infectious-Recovered-Susceptible (SIRS) model\, which is co
 mmonly used by modellers. Finally\, we show how our model can be applied t
 o SARS-CoV-2 Omicron variant\, making use of parameter values from the ric
 h COVID-19 literature. \n
LOCATION:Zoom
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