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SUMMARY:Stochastic Epidemic Models with Partial Information : Dark Figure
and Parameters Estimation
DTSTART;VALUE=DATE-TIME:20220805T073000Z
DTEND;VALUE=DATE-TIME:20220805T075000Z
DTSTAMP;VALUE=DATE-TIME:20231210T043151Z
UID:indico-contribution-1232@conference2.aau.at
DESCRIPTION:Mathematical models of epidemics such as the current COVID-19
pandemics often use compartmental models dividing the population into seve
ral compartments. Based on a microscopic setting describing the temporal e
volution of the subpopulation sizes in the compartments by stochastic coun
ting processes one can derive macroscopic models for large populations des
cribing the average behavior by associated ODEs such as the celebrated SIR
model. Further\, diffusion approximations allow to address fluctuations f
rom the average and to describe the state dynamics also for smaller popula
tions by stochastic differential equations (SDE).\nUsually not all of the
state variables are directly observable and we are facing the so-called
“dark figure” problem addressing for example the unknown number of asy
mptomatic and non-detected infections. Such not directly observable states
are problematic if it comes to the computation of characteristics of the
epidemic such as the effective reproduction rate and the prevalence of the
infection within the population. Further\, the management and containment
of epidemics relying on solutions of (stochastic) optimal control problem
s and the associated feedback controls need observations of the current st
ate as input.\nThe estimation of unobservable states based on records of t
he observable states leads to a non-standard filtering problem for observa
ble stochastic models. We adopt the extended Kalman filter approach coping
with non-linearities in the state dynamics and the state-dependent diffus
ion coefficients in the SDEs. This allows to develop approximative solutio
ns to that filtering problem.\nThe proposed model depends on a variety of
parameters that can be time-dependent and have been calibrated to real-wor
ld data for COVID-19. There\, we apply maximum-likelihood and Kalman filte
r methods. We illustrate our theoretical finding by numerical results.\n\n
https://conference2.aau.at/event/131/contributions/1232/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1232/
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