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CATEGORIES:Talk
DESCRIPTION:Matthew Wascher\, of the Ohio State University\, will be delive
ring this week's mathematics colloquium.\n\n \n\nAbstract: The (classical)
contact process\, or SIS epidemic\, is a model for the spread of disease th
rough a population. We model the population with a graph\, where vertices r
epresent individuals and directed edges represent potential pathways for in
fection to spread. At any given time\, each vertex is either "infected" or
"healthy\," and given an infection rate parameter \, the process evolves ac
cording to the following dynamics. Each infected vertex infects each of its
out-neighbors at rate . Simultaneously\, each infected vertex become healt
hy at rate 1. This model is known to exhibit a phase transition in for man
y graphs\, such as the nearest-neighbor lattice Z. This means that there ex
ists a value _c such that the long term survival behavior of the epidemic w
hen <_c differs from this behavior when >_c.\n\nWe consider a modified cont
act process that we call the contact process with\navoidance. The process r
etains the infection and recovery dynamics of the\nclassical contact proces
s\, but in addition each healthy vertex can avoid each\nof its infected nei
ghbors at rate by turning off the directed edge from\nthat infected neighb
or to itself until the infected neighbor recovers. This\nmodel presents a c
hallenge because\, unlike the classical contact process (=0)\, it has not b
een shown to be an attractive particle system. We study the\nsurvival dynam
ics of this model on the nearest-neighbor lattice Z\, the cycle\nZ_n\, and
the star graph. On Z\, we show there is a phase transition in \nbetween alm
ost sure extinction and positive probability of survival. On Z_n\, we\nshow
that as the number of vertices n\, there is a phase transition\nbetween lo
g and exponential survival time in the size of the graph. On the star\ngrap
h\, we show that as n the survival time is polynomial in n for\nall values
of and . This contrasts with the classical contact\nprocess where the surv
ival time on the star graph is exponential in n for all\nvalues of .
DTEND:20191101T200000Z
DTSTAMP:20230322T130655Z
DTSTART:20191101T190000Z
GEO:38.21389;-85.759743
LOCATION:Natural Sciences Building\, 212D
SEQUENCE:0
SUMMARY:Mathematics Colloquium: Matthew Wascher\, "A phase transition for t
he contact process with avoidance on Z\, Z_n\, and the star graph"
UID:tag:localist.com\,2008:EventInstance_31761301946533
URL:https://events.louisville.edu/event/mathematics_colloquium_matthew_wasc
her_a_phase_transition_for_the_contact_process_with_avoidance_on_z_z_n_and_
the_star_graph
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