Mathematics Colloquium
Tom Chou
UCLA
Title: New applications and extensions of classic structured population models: birth control, drug addiction, and kinetic theory
Date: Friday October 27, 2023
Place and Time: Love 101, 3:05-3:55 pm
Abstract. I will briefly review a few new applications of structured population PDEs (based mainly on the classical deterministic age-structured McKendrick model), including a retrospective analysis of the one-child birth policy, models for forecasting drug deaths, and sizer-timer-adder mechanisms of cell division. These applications highlight applications of existing mathematical approaches in novel ways and motivate the development of new methods. Then, I will present a stochastic framework of structured population models that is developed using ideas from kinetic theory. The high-dimensional kinetic equations can be marginalized in different ways to define PDEs for different moments and correlations that can be closed if if parameters of an individual are independent of the age of other individuals. The kinetic theory is shown to unify master equation frameworks with deterministic age-dependent (non-Markovian) birth and death rate models. The new kinetic theory can be further extended to track multiple attributes (such as a whole panel of gene expression levels) and generational subpopulations. Applications of this type of kinetic theory to cell development are currently being studied.