Date of Award

9-2011

Document 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.

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