colloquium

Biological systems often exhibit strongly nonlinear dynamics, such as slow–fast manifold oscillations, making accurate state-space estimation from noisy measurements particularly challenging. Classical state-space estimation methods, such as Kalman–Bucy and particle filters, either rely on restrictive Gaussian assumptions or become computationally prohibitive in high-dimensional settings. In this talk, I present two complementary approaches to nonlinear, high-dimensional data assimilation. First, I introduce an adaptive Gaussian mixture filter that splits and merges Gaussian particles to efficiently capture asymmetric and highly nonlinear state distributions. Second, I present a score-based filter that integrates score-based generative modeling with a forward process derived from the measurement equation, enabling analytically tractable likelihood updates and improved stability in high dimensions. Together, these methods provide scalable and accurate frameworks for state estimation in complex biological dynamical systems.

Classical epidemic models treat transmission parameters as fixed and populations as well mixed. In practice, however, epidemic dynamics are shaped by population structure, behavioural decision-making, and adaptive learning. In this talk, I present a mathematical framework that integrates these components within a unified dynamical perspective. We begin with a structured SEIRL model and revisit the basic reproduction number as the spectral radius of a next-generation operator. We then introduce a game-theoretic viewpoint in transmission dynamics, specifically touching on how vaccination may lend itself to be modelled by classic Nash games, and then how compliance with non-pharmaceutical interventions across interacting population groups may arise as Nash equilibria of a multi-player game. Finally, we consider adaptive ensemble forecasting methods formulated as constrained optimization problems over expanding time windows, and showcase the AI4Casting Hub. I conclude by discussing open questions concerning stability, equilibrium selection, and the analysis of adaptive epidemic models.