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SUMMARY:Household epidemic models and McKean-Vlasov Poisson driven SDEs -
Raphaël Forien (INRA\, Avignon)
DTSTART;VALUE=DATE-TIME:20200224T120000Z
DTEND;VALUE=DATE-TIME:20200224T130000Z
UID:https://talks.ox.ac.uk/talks/id/a6b59c04-5fc4-4edb-9269-7b69eac44e69/
DESCRIPTION:In this talk I will present an epidemic model where susceptibl
e and infected individuals are distributed in discrete households of finit
e size. Infected individuals can either infect other individuals in the sa
me household or individuals chosen uniformly in the whole population. When
the number of households tends to infinity\, we obtain a limit for the ep
idemic process given in terms of a nonlinear Markov process which solves a
McKean-Vlasov Poisson driven SDE. We also prove a propagation of chaos re
sult. Finally\, we define a basic reproduction number R0\, and show that i
f R0>1\, then the nonlinear Markov process has a unique non trivial ergodi
c invariant probability measure (i.e. the epidemic spreads to a large prop
ortion of the population with positive probability)\, whereas if R0<=1\, t
he non-linear Markov process converges to 0 as t tends to infinity (the ep
idemic quickly dies out). To conclude I will mention some results on the f
luctuations of the epidemic process.\n\nThis is joint work with Étienne P
ardoux.\nSpeakers:\nRaphaël Forien (INRA\, Avignon)
LOCATION:Mathematical Institute (L4)\, Woodstock Road OX2 6GG
URL:https://talks.ox.ac.uk/talks/id/a6b59c04-5fc4-4edb-9269-7b69eac44e69/
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DESCRIPTION:Talk:Household epidemic models and McKean-Vlasov Poisson drive
n SDEs - Raphaël Forien (INRA\, Avignon)
TRIGGER:-PT1H
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