Modeling COVID-19 Dynamics in German States Using Physics-Informed Neural Networks

TL;DR

This work applies Physics-Informed Neural Networks to solve the inverse SIR problem using RKI data across all 16 German states over 1200 days, yielding state-specific transmission $\beta$, recovery $\alpha$, and time-varying $\mathcal{R}_t$. The authors validate their PINN approach against a damped-Newton baseline and then perform a two-stage estimation to obtain both time-independent and time-dependent parameters, with robust repetition. Key findings show regional differences in transmission linked to vaccination uptake, and that $\mathcal{R}_t$ captures major pandemic phases such as Omicron, while state-specific recovery dynamics influence peak transmission. The results demonstrate the practical utility of PINNs for localized, long-term epidemiological analysis and provide a data-driven framework for sub-national pandemic assessment and policy evaluation, with potential extensions to more complex models and additional data streams.

Abstract

The COVID-19 pandemic has highlighted the need for quantitative modeling and analysis to understand real-world disease dynamics. In particular, post hoc analyses using compartmental models offer valuable insights into the effectiveness of public health interventions, such as vaccination strategies and containment policies. However, such compartmental models like SIR (Susceptible-Infectious-Recovered) often face limitations in directly incorporating noisy observational data. In this work, we employ Physics-Informed Neural Networks (PINNs) to solve the inverse problem of the SIR model using infection data from the Robert Koch Institute (RKI). Our main contribution is a fine-grained, spatio-temporal analysis of COVID-19 dynamics across all German federal states over a three-year period. We estimate state-specific transmission and recovery parameters and time-varying reproduction number (R_t) to track the pandemic progression. The results highlight strong variations in transmission behavior across regions, revealing correlations with vaccination uptake and temporal patterns associated with major pandemic phases. Our findings demonstrate the utility of PINNs in localized, long-term epidemiological modeling.

Figures (7)

• Figure 1: Higher vaccination coverage coincides with lower pandemic effects. (Left): The correlation between the vaccination rate and the corresponding mean transmission rate $\beta$ for each federal state. (Right): The correlation between the vaccination rate and the peak $\mathcal{R}_t\xspace$ value for each state.
• Figure 2: Visualization of the recovery rate $\alpha$ and the transmission rate $\beta$ for each federal state (MWP=Mecklenburg-Western Pomerania) compared to the mean values of $\alpha$ and $\beta$ for Germany.
• Figure 3: Visualization of the time-dependent reproduction number $\mathcal{R}_t\xspace$ over the pandemic for Germany on top, followed by various states. In all cases, we show results for $\alpha = 1/14$WHO and our experimentally determined state-specific recovery rate $\alpha_{\text{exp}}$. Events COVIDChronik like the peak of specific virus variants or the start of the vaccination campaigns are marked horizontally. The remaining states are included in the supplementary material.
• Figure 4: Visualization of the real numbers of infectious individuals in Germany and the prediction of the training with $\alpha=0.07$ for the time span between February 13, 2020, and March 19, 2020.
• Figure 5: All visualizations of the $\mathcal{R}_t\xspace$ value from \ref{['sec:rt_exp']}. (part 1)