Abstract:
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates. We present a semi-Markov stochastic model of populations that incorporate age-dependent birth, death, and fission rates. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth, death, and fission. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a BBGKY-like hierarchy. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.
Biography:
Tom Chou is Professor in the Department of Biomathematics and the Department of Mathematics at UCLA, Los Angeles. Professor Chou holds a Ph.D. in Physics from Harvard University. He works on applied math, mathematical biology, theoretical soft condensed matter, and statistical mechanics problems.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai