MEmilio: a high performance Modular EpideMIcs simuLatIOn software for multi-scale and comparative simulations of infectious disease dynamics

Automated Discovery of Spatio-Temporal Epidemic Patterns via Hybrid Evolutionary-PDE Frameworks

We introduce a hybrid computational framework for the automated discovery of complex dynamic regimes in spatially distributed epidemiological models. Traditional models often fail to capture the rich spatio-temporal heterogeneity of disease spread, while high-dimensional Partial Differential Equation (PDE) models suffer from the “curse of dimensionality” during parameter calibration. To address this, we couple a Differential Evolution (DE) search engine with a Just-In-Time (JIT) compiled Finite Difference solver, resulting in a hybrid architecture that performs “Simulation-Based Inference”. This method navigates the parameter space to identify regimes that generate specific emergent behaviors, such as Turing patterns, traveling wave competition, and resonance-driven outbreaks. We apply our method to a spatial Susceptible-Infected-Recovered-Susceptible (SIRS) model featuring seasonal forcing and heterogeneous diffusion. Our results demonstrate that the JIT-compiled solver achieves a $\sim 9 \times$ speedup compared to vectorized NumPy implementations, rendering the evolutionary exploration of PDEs computationally feasible and validating the system's ability to discover worst-case epidemic scenarios and geometric interference patterns without reliance on manual analytical derivation.

Epidemic Spread and Control Strategies: A Spatial-individual Agent-based Modeling and Optimization Approach.

Epidemic Threshold Analysis of an SEIMQR Model Incorporating Healthcare Resource Constraints

Introduction Epidemic models commonly assume unlimited healthcare resources and overlook a critical operational reality: healthcare system overload reduces recovery rates and amplifies outbreak severity. We propose an enhanced susceptible-exposed-infected-mutant-quarantined-recovered (SEIMQR) model that explicitly links the recovery process to time-varying hospital-bed availability, and thereby better reflects practical healthcare constraints. Methods The model integrates a saturating, resource-dependent recovery function and uses the quarantine rate as the primary control parameter. We performed a systematic dynamic analysis using bifurcation theory and validated the model through numerical simulations and empirical coronavirus disease 2019 (COVID-19) surveillance data from the United Kingdom. These data covered distinct phases of the pandemic. Results Our analysis identified a precise quarantine threshold (\begin{document}$ \delta =0.573595 $\end{document}) that distinguishes disease elimination from endemic persistence. Simulation results show that strengthening quarantine measures effectively suppresses the epidemic scale. Furthermore, the model fit the reported cumulative case data with high accuracy across different variant-dominant periods and policy regimes, which demonstrates its adaptability. Conclusion These findings quantify a critical intervention threshold and illustrate the synergistic relationship between medical capacity and quarantine intensity. This study provides a theoretically grounded, resource-aware framework for guiding integrated public health strategies when healthcare resources are finite. Therefore, it supports more realistic epidemic preparedness and response planning.

Efficient stochastic epidemic simulation via the Sellke construction

Stochastic epidemic models are a cornerstone of infectious disease epidemiology and are often used to study intervention scenarios. However, large run-to-run variability can make intervention effects difficult to estimate precisely. We revisit the epidemic Sellke construction, which assigns each individual an infection threshold for the cumulative infection hazard such that, conditional on the thresholds, the epidemic trajectory becomes deterministic. This enables coupling of simulations with and without an intervention, yielding low-variance effect estimates even when outcomes such as final size or peak incidence vary widely between runs. We develop an exact, event-driven implementation that maintains infection and recovery events in priority queues. Cumulative infection-hazard updates require O(log N) time per event, yielding overall complexity O(Elog N) for E events in a population of size N. The implementation achieves computational performance comparable to the classical Gillespie algorithm while naturally accommodating non-Markovian infectious periods and complex infectiousness profiles. We illustrate the approach using distance-dependent spread of avian influenza between poultry farms in the Netherlands and a multilayer population with households, schools, and workplaces. In both examples, coupling enables efficient within-run comparisons of intervention scenarios across stochastic realisations.

GENIE: Generative Neural Inference for Epidemics

This work introduces Generative Neural Inference for Epidemics (GENIE), a spatio-temporal ML-based framework for high-resolution forecasting of the burden of respiratory pathogens and demonstrates superior performance across a range of measures.

A Network-Based Epidemic Simulation Model for Assessing Non-pharmaceutical Interventions