Positivity-preserving methods for population models

Speaker: Prof. Dr. Arieh Iserles
Affiliation: University of Cambridge, UK
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Abstract. For good phenomenological reasons, the vector field of many ODEs of chemical kinetics and population dynamics (not least the SIR model of epidemiology) are related to graph Laplacians and this accounts for their qualitative features, not least the conservation of positivity and mass. Respecting positivity under discretization, though, is notoriously difficult. In this talk, we introduce a new approach, based on Lie-group methods for graph Laplacians, and explore its features and potential. We also explore the conditions allowing to write a polynomial ODE system in the form y’ = A(y) y, where the matrix A(y) is a graph Laplacian.

This is joint work with Sergio Blanes and Shev Macnamara.