Jason Harmon (UCF School of Data, Mathematical, and Statistical Sciences) will speak on "Impacts of Varying Dispersal in Metapopulation Models" at this week's seminar.
Abstract: Multipatch models effectively capture population and disease dynamics across heterogeneous environments, where long-term persistence depends heavily on network topology and dispersal connectivity. Analytically assessing persistence requires evaluating the spectral abscissa of the system’s Jacobian matrix at a boundary equilibrium. While this evaluation is highly complex for general net- works, fast dispersal regimes allow the spectral abscissa to be expanded via perturbation using the group inverse, a specialized generalized inverse, of the underlying graph’s Laplacian Matrix. This talk presents framework utilizing Sherman–Morrison-type formulas tailored for group invertible matrices to analyze the changes in spectral abscissa due to changes in dispersal between two patches. Utilizing this formulation, we demonstrate how localized variations in dispersal intensity reshapes the overall population growth rate and persistence thresholds.
Short Bio: Jason Harmon is a fourth-year graduate student pursuing a PhD in Mathematics at the University of Central Florida’s School of Data, Mathematical and Statistical Sciences. His research focuses on mathematical epidemiology, dynamical systems, and generalized inverses. He earned his Bachelor's degree in Mathematics at the University of Central Florida’s former Department of Mathematics and has presented his work at MCA 2025 and SIAM 2026.
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