Machine Learning for Mechanistic Models of Metapopulation Dynamics

Mathematical models in ecology and epidemiology must be consistent with observed data in order to generate reliable knowledge and sound policy. Metapopulation systems, which consist of a collection of sub-populations at various locations, pose technical challenges in statistical inference due to nonlinear, stochastic interactions. Difficulties encountered in these methodological issues can obstruct the core scientific questions concerning the link between the mathematical models and the data. Progress in statistically efficient simulation-based inference for partially observed stochastic dynamic systems has enabled the development of statistically rigorous approaches to the analysis of nonlinear but low-dimensional systems. Recently, an algorithm has been developed which enables comparable inference for higher-dimensional models arising in metapopulation systems. The COVID-19 pandemic provides a situation where mathematical models and their policy implications were widely visible, and we revisit an influential metapopulation model used to inform basic epidemiological understanding early in the pandemic. Our methods support self-critical data analysis, enabling us to identify and address model limitations, and leading to a new model with substantially improved statistical fit and parameter identifiability. Our results suggest that the lockdown initiated on January 23, 2020 in China was more effective than previously thought. We proceed to recommend statistical analysis standards for future metapopulation system modeling.