Jason Harmon will present “Impact of varying dispersal in metapopulation models: A new type of Sherman-Morrison formula“ at this week's Mathematical Biology Seminar.
Abstract: For populations and diseases distributed across patches in heterogeneous environments, meta-population models are a useful tool. It's of particular interest whether populations and diseases will persist depending on dispersal rates and network connectivity. In particular, we investigate how changes in network structure and dispersal intensity impact the long-term population growth rate and determine the population persistence threshold.
The population growth rate can be found via the largest real part of the eigenvalues of the Jacobian. This eigenvalue can be approximated by expanding in terms of the Group Inverse. The Group Inverse is a generalized inverse for a specific class of matrices, including the discrete Laplacian. We propose a Sherman-Morrison type formula that can be used to find an updated group Inverse for varying dispersal. Using this formula, we explore how changes in dispersal affect the population growth rate.
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