Dr. B Sagar (UCF School of Data, Mathematical, and Statistical Sciences) will speak on "New Insights into Lyapunov Functions in Mathematical Epidemiology" at this week's seminar.
Abstract: Lyapunov functions play a central role in establishing global stability in mathematical epidemiology, but their construction remains one of the most challenging aspects of stability analysis. In this work, we introduce a new idea for constructing and applying Lyapunov functions and demonstrate its effectiveness in a multi-group, multi-stage epidemic model. The approach provides a different route to establishing global stability and reveals a structure that is not immediately apparent from standard Lyapunov constructions. More broadly, this idea may provide a useful direction for addressing other global stability problems that remain unresolved.
Short Bio: Dr. Sagar is a STEM postdoctoral researcher in the School of Data, Mathematical, and Statistical Sciences at the University of Central Florida. His current research focuses on mathematical epidemiology, dynamical systems, Lyapunov methods, and computational PDEs. He earned his PhD in Applied Mathematics from the National Institute of Technology Rourkela, with research on meshless numerical methods, radial basis functions, and fractional partial differential equations. He was a Halloran Scholar at SISMID, Emory University, and was selected for the SIAM Mathematical Problems in Industry Workshop and the OneMath World School in Mathematical Biology.
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