Catching a wave: Incorporating space for more precise epidemiological modeling of disease spread
Understanding what challenges organisms face in rapidly changing environments is crucial, especially in the context of global climate change. A new study led by AIAS Fellow Anna M. Langmüller investigates the conditions under which it is crucial to incorporate spatial structure into epidemiological models to obtain more accurate predictions of disease spread in time and space.


Since their introduction nearly a century ago, ordinary differential equation models, such as the classic Susceptible-Infectious-Recovered (SIR) model, have been widely used in epidemiology to study and predict the spread of disease. A major simplifying assumption of these models is that populations are homogeneously mixed, meaning that the risk of infection is equal for all individuals in a population. The reaction-diffusion model on the other hand offers an alternative modeling approach that allows epidemiologists to describe disease dynamics in spatially continuous populations where individuals move randomly.
Development of a critical threshold
In a new study in the scientific journal Theoretical Population Biology, Anna M. Langmüller and collaborators explore the conditions under which spatial structure needs to be accounted for, and when the simplifying assumption of homogeneous mixing is adequate. For this, the team of researchers have derived a critical threshold for the diffusion coefficient – which determines the individual dispersal – below which disease dynamics become spatially heterogeneous. The development of this threshold provides applied disease modelers with a relatively simple calculation they can use to evaluate whether spatial heterogeneity must be included in their simulation models.
The importance of spatial factors
The analytical findings in the study are validated by using an individual-based simulation framework implemented in an open-source simulator called SLiM (https://messerlab.org/slim/). This simulator has enabled the team of researchers to confirm their analytical expectations that once individual dispersal falls below the critical threshold, key epidemiological metrics such as the severity and duration of an epidemic become dependent on the level of individual dispersal.
The new study shows the importance of carefully considering spatial factors in epidemiological modeling and highlights the potential pitfalls associated with design choices in individual-based models of disease dynamics.
Access the full scientific article here
Catching a wave: On the suitability of traveling-wave solutions in epidemiological modeling' by Anna M. Langmüller et al in: Theoretical Population Biology, 18 January 2025:
https://www.sciencedirect.com/science/article/pii/S0040580924001072?via%3Dihub
Funding
Anna M. Langmüller and this study have received funding from the European Union’s Horizon2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 101025586.
Contact
Anna Langmüller, AIAS-AUFF Fellow
E-mail: annamaria.langmueller@aias.au.dk
Aarhus Institute of Advanced Studies, AIAS
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