Hybrid frameworks for accurate and efficient simulation of epidemiological processes

Kurzfassung

Mathematical epidemiological models are essential for studying transmission dynamics of infectious diseases and supporting public health decision-making. These models range from deterministic mean-field approaches, to metapopulation models and detailed individual-based models. Selecting the appropriate modeling framework is a non-trivial task and depends on research objective, data availability, and computational constraints. Especially in highly stochastic regimes, the computational cost can become prohibitive as numerous simulations are required to reliably approximate the full probability distribution. While mean-field methods reduce this demand, they fail to capture the stochasticity inherent in such systems. Hybrid modeling approaches aim to balance this trade-off between accuracy and computational efficiency. In this work, we present two hybrid frameworks that combine stochastic individual-based models with deterministic equations-based methods. The first framework implements a per-simulation switch based on a single sample trajectory. The second combines stochastic simulation with the Method of Moments (MoM) utilizing moment equations to describe the dynamics of the mean and higher order central moments of a stochastic process. While the MoM-based model allows for the switching condition to be evaluated against the probability distribution rather than a single realization, it requires moment closure methods to resolve higher-order dependences. We apply both approaches to a spatially-resolved stochastic Susceptible-Infected-Recovered (SIR) model and analyze their performance and computational effort under varying conditions. Furthermore, we compare different switching criteria for transitioning between the stochastic and deterministic components of the hybrid model. Overall, our results demonstrate that these hybrid modeling frameworks significantly outperform the purely deterministic approach while substantially reducing computational costs compared to the fully stochastic model. ¬