Research Seminar - Ralf Wunderlich
We are pleased to announce the upcoming Research Seminar on January 19, 2024.
The Institute for Statistics and Mathematics is pleased to invite you to the next research seminar, taking place on campus:
Ralf Wunderlich (Institute of Mathematics, BTU Brandenburg University of Technology Cottbus-Senftenberg)
Stochastic Models and Optimal Control of Epidemics Under Partial Information
Friday, January 19, 2024, 10:30 am, Building D4, Room D4.0.127
Mathematical models of epidemics such as the COVID-19 pandemics often use compartmental models dividing the population into several compartments. Based on a microscopic setting describing the temporal evolution of the subpopulation sizes in the compartments by stochastic counting processes one can derive macroscopic models for large populations describing the average behavior by associated ODEs such as the celebrated SIR model. Further, diffusion approximations allow to address fluctuations from the average and to describe the state dynamics also for smaller populations by stochastic differential equations (SDE).
Usually 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 asymptomatic 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 problems and the associated feedback controls need observations of the current state as input.
The estimation of unobservable states based on records of the observable states leads to a non-standard filtering problem for partially observable stochastic models. We adopt the extended Kalman filter approach coping with non-linearities in the state dynamics and the state-dependent diffusion coefficients in the SDEs. Based on these filtering results we study a stochastic optimal control problem under partial information arising in the cost-optimal management of epidemics.
We aim to stream all on-campus talks via Zoom. A direct link to the stream will be posted on our website.
For further information and the seminar schedule, please see: