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SUMMARY:A structured population model with diffusion in structure space
DTSTART;VALUE=DATE-TIME:20180712T003000Z
DTEND;VALUE=DATE-TIME:20180712T005000Z
DTSTAMP;VALUE=DATE-TIME:20220819T205732Z
UID:indico-contribution-491@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Fabio A. Milner (School of Mathematical and Statisti
cal Sciences\, Arizona State University)\nA structured population model is
described and analyzed\, in which individual dynamics is stochastic. The
model consists of a PDE of advection-diffusion type in the structure varia
ble. The population may represent\, for example\, the density of infected
individuals structured by pathogen density $x$\, $x\\ge0$. The individuals
with density $x=0$ are not infected\, but rather susceptible or recovered
. Their dynamics is described by an ODE with a source term that is the exa
ct flux from the diffusion and advection as $x\\to0^+$. Infection/reinfect
ion is then modelled moving a fraction of these individuals into the infec
ted class by distributing them in the structure variable through a probabi
lity density function. Existence of a global-in-time solution is proven\,
as well as a classical bifurcation result about equilibrium solutions: a n
et reproduction number $R_0$ is defined that separates the case of only th
e trivial equilibrium existing when $R_01$. Numerical simulation results a
re provided to show the stabilization towards the positive equilibrium whe
n $R_0>1$ and towards the trivial one when $R_0\n\nhttps://conferences.mat
hs.unsw.edu.au/event/2/contributions/491/
LOCATION:University of Sydney New Law School/--107
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/491/
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