Stochastic epidemic models with memory, varying
infectivity/susceptibility and waning immunity
October 11, 2023
3:00 pm PGH 646
Abstract
In this talk we will discuss several stochastic epidemic models
recently developed to account for general infectious durations,
infection-age dependent infectivity and/or progress loss of
immunity/varying susceptibility, extending the standard epidemic
models. We construct individual based stochastic models, and prove
scaling limits for the associated epidemic dynamics in large
populations. Each individual is associated with a random
function/process that represents the infection-age dependent
infectivity force to exert on other individuals. We extend this
formulation to associate each individual with a random function that
represents the loss of immunity/varying susceptibility. A typical
infectivity function first increases and then decreases from the epoch
of becoming infected to the time of recovery, while a typical
immunity/susceptibility function gradually increases from the time of
recovery to the time of losing immunity and becoming susceptible. The
scaling limits are deterministic and stochastic Volterra integral
equations. We present some new PDEs models arising from the scaling
limits. We also discuss some spatial models with varying infectivity
and the associated scaling limits and PDE models. (This talk is based
on joint work with Etienne Pardoux, Raphael Forien, and Arsene Brice
Zosta Ngoufack.)
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