Kinetic Theories of Age-structured Replication-decay Processes

Thursday, July 23, 2015 - 9:00am - 9:50am
Lind 305
Tom Chou (University of California, Los Angeles)
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
system-size-dependent birth and death rates. Stochastic theories that
treat semi-Markov age-dependent processes using e.g., the
Bellman-Harris equation, cannot resolve a population's age-structure
and are unable to quantify population-size dependencies. In this talk,
I will present a systematic derivation of a new fully stochastic
kinetic theory for interacting age-structured particles. By defining
multiparticle probability density functions, we derive a hierarchy of
kinetic equations for the stochastic evolution of an ageing population
undergoing birth and death. 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. However, explicit solutions are derived
in two simple limits and compared with their corresponding mean-field
results. Our results generalize both deterministic models and
existing master equation approaches by providing an intuitive and
efficient way to simultaneously model age- and system-size-dependent
stochastic dynamics
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