[Todos CMAT] Seminario de Probabilidad y Estadística

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Mie Dic 9 10:30:28 -03 2020

Seminario de Probabilidad y Estadística

Título: "A Computational Framework for Evaluating the Role of Mobility on the Propagation of Epidemics on Point Processes"

Expositor: F. Baccelli (INRIA)

This work is focused on SIS epidemic dynamics (also known as the contact
process) on stationary Poisson point processes of the Euclidean plane, when the
infection rate of a susceptible point is proportional to the number of infected
points in a ball around it. Two models are discussed, the first with a static
point process, and the second where points are subject to some random motion.
For both models, we use conservation equations for moment measures to analyze
the stationary point processes of infected and susceptible points. A heuristic
factorization of the third moment measure is then proposed to derive simple
polynomial equations allowing one to derive closed form approximations for the
fraction of infected nodes and the steady state. These polynomial equations also
lead to a phase diagram which tentatively delineates the regions of the space of
parameters (population density, infection radius, infection and recovery rate,
and motion rate) where the epidemic survives and those where there is
extinction. According to this phase diagram, the survival of the epidemic is not
always an increasing function of the motion rate. These results are
substantiated by simulations on large two-dimensional tori. These simulations
show that the polynomial equations accurately predict the fraction of infected
nodes when the epidemic survives. The phase diagram is also partly substantiated
by the simulation of the mean survival time of the epidemic on large tori. The
phase diagram accurately predicts the parameter regions where the mean  survival
time increases or decreases with the motion rate.

F. Baccelli and N. Ramesan (INRIA and UT Austin)
Viernes 11/12 a las 10:30, https://salavirtual-udelar.zoom.us/j/2301522749

Contacto: Alejandro Cholaquidis - acholaquidis en hotmail.com


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