Date of Award
9-2011
Document type
dissertation
Access Type
Open Access Dissertation
Degree Name
Doctor of Philosophy (PhD)
Degree Program
Mathematics
First Advisor
Panayotis Kevrekidis
Second Advisor
Anna Liu
Third Advisor
Alan Perelson
Subject Categories
Mathematics | Statistics and Probability
Abstract
In this thesis we develop a mathematical model to describe HIV-1 evolution during the first stages of infection (approximately within 40-60 days since onset), when one can assume exponential growth and random accumulation of mutations under a neutral drift. We analyze the Hamming distance (HD) distribution under different models (synchronous and asynchronous) in the absence of selection and recombination. In the second part of the thesis, we introduce recombination and develop a combinatorial approach to estimate the new HD distribution. We conclude describing a T statistic to test significance differences between the HD of two genetic samples, which we derive using U-statistics.
DOI
https://doi.org/10.7275/2389569
Recommended Citation
Giorgi, Elena Edi, "A Mathematical Growth Model of the Viral Population in Early HIV-1 Infections" (2011). Open Access Dissertations. 458.
https://doi.org/10.7275/2389569
https://scholarworks.umass.edu/open_access_dissertations/458