Computational and Applied Math Proseminar

Thursday, April 21, 2005, 3:40 p.m. PSA 102

David Bortz

Math Biology Research Group, Univ of Michigan

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