Graduate student Kasia Pawelek publishes her research in Mathematical Biosciences

Kasia Pawelek is a graduate student who recently defended her dissertation in the Applied Mathematical Sciences PhD Program. She published part of her research in an article A model of HIV-1 infection with two time delays: Mathematical analysis and comparison with patient data in the January 2012 issue of Mathematical Biosciences (Volume 235, Pages 98-109). Also an author on the paper is Pawelek’s dissertation advisor, Assistant Professor Libin Rong of the Department of Mathematics and Statistics. The abstract of the paper is given below.

“Mathematical models have made considerable contributions to our understanding of HIV dynamics. Introducing time delays to HIV models usually brings challenges to both mathematical analysis of the models and comparison of model predictions with patient data. In this paper, we incorporate two delays, one the time needed for infected cells to produce virions after viral entry and the other the time needed for the adaptive immune response to emerge to control viral replication, into an HIV-1 model. We begin model analysis with proving the positivity and boundedness of the solutions, local stability of the infection-free and infected steady states, and uniform persistence of the system. By developing a few Lyapunov functionals, we obtain conditions ensuring global stability of the steady states. We also fit the model including two delays to viral load data from 10 patients during primary HIV-1 infection and estimate parameter values. Although the delay model provides better fits to patient data (achieving a smaller error between data and modeling prediction) than the one without delays, we could not determine which one is better from the statistical standpoint. This highlights the need of more data sets for model verification and selection when we incorporate time delays into mathematical models to study virus dynamics.”

Pawelek’s research was supported by a grant from the National Science Foundation (DMS-1122290) to Rong, and a National Institutes of Health P30 grant to establish a Core Center in Quantitative Biology.