@phdthesis{OuaboKamkumo2025, author = {Ouabo Kamkumo, Florent}, title = {Stochastic epidemic models with partial information and dark figure estimation}, doi = {10.26127/BTUOpen-7197}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-71976}, school = {BTU Cottbus - Senftenberg}, year = {2025}, abstract = {This thesis presents a novel stochastic modeling framework for epidemic dynamics, focusing on the challenges posed by non-observable states and the gradual decline of immunity, as revealed by the Covid-19 pandemic. Our research develops an extended compartmental model that incorporates sequences of cascade states to accurately represent the progressive loss of immunity after vaccination or recovery. This model, rooted in a non-homogeneous continuous-time Markov chain and approximated by a diffusion process, facilitates efficient computation. The resulting dynamics exhibit non-linearities in both the drift and diffusion coefficients, making the process of hidden state estimation particularly challenging. These complexities highlight the need for advanced techniques to accurately capture and predict the system's behavior under partial observability. A novel approach using cascade states is introduced to tackle the issue of partially hidden compartments where either inflow or outflow is observed, but not both. By leveraging information from observed transitions, this method significantly enhances model accuracy. The framework also enables the application of advanced filtering techniques, particularly the Extended Kalman Filter (EKF), for estimating both hidden epidemic states and time-varying parameters. This allows for calibrating based on real data, ensuring robust and accurate predictions. Furthermore, this thesis extends the methodology to multi-group (multi-patch) models, capturing the complexities of heterogeneous population dynamics. This includes factors such as mobility, super-spreader events, and accounting for partial information. By incorporating these elements, the model provides a more comprehensive understanding of epidemic spread across diverse and interconnected populations. To address the curse of dimensionality often encountered in high-dimensional filtering problems, a modified EKF based on a reduced-order EKF is introduced, leveraging a low-rank approximation of the covariance matrix. This reduced-order EKF allows for stable and efficient estimation of hidden states even with limited computational resources. Finally, the work explores parameter estimation within the partial information context, employing both likelihood-based inference and state augmentation techniques. Numerical experiments demonstrate the model's ability to accurately reproduce observed Covid-19 dynamics in Germany, highlighting its potential for informing public health strategies and managing future outbreaks. This work offers a robust and adaptable framework for understanding and predicting the spread of infectious diseases.}, subject = {Compartmental model; Stochastic model; Partial information; Extended Kalman filter; Parameter estimation; Kompartimentmodell; Stochastisches Modell; Teilinformationen; Erweiterter Kalman Filter; Parametersch{\"a}tzung; Stochastische optimale Kontrolle; Kompartimentmodell; Kalman-Filter; Partielle Information}, language = {en} }