Thursday,
April 21, 2005, 3:40 p.m. PSA 102
Identification and Analysis of Differential Equation Models
of HIV Infection Dynamics
Abstract
In this talk, we will consider mathematical and statistical
issues which arise when modeling HIV pathogenesis. Many models
have been proposed to describe HIV infection dynamics during
anti-retroviral therapy and we will present results from our
development and application of a methodology to provide stochastic
evidence for specific mathematical forms of the model.
Specifically, we will present results concerning the existence
of latently infected cells as well as the delay between infection
and production of virions in HIV pathogenesis (under reverse
transcriptase and protease inhibitor therapy). We will also
discuss the numerical issues encountered in performing this
computation.
Time permitting, I will also comment on the statistical distribution
2) the image reconstructions based on the wiggly Fourier images.
of the delay across the population of HIV virions and CD4 cells
(suggesting the existence of probability measure-dependent dynamics).
To study systems such as these, we have developed a mathematical
framework (employing results from probability theory involving the
Prohorov metric and the Helly-Bray theorem) to establish well-posedness
for both the forward and inverse problems.
Though we will illustrate our methodology within the context of
HIV infection dynamics, it has relevance to a wide variety of
applications with similar mathematical and statistical properties.
For further information please contact:
mittelmann@asu.edu