A Mathematical Growth Model of the Viral Population in Early Hiv-1 Infections

A MATHEMATICAL GROWTH MODEL OF THE VIRAL POPULATION IN EARLY HIV-1 INFECTIONS SEPTEMBER 2011 ELENA EDI GIORGI, ”Laurea,” UNIVERSITA’ DI PISA M.S., UNIVERSITY OF MASSACHUSETTS AMHERST M.S., UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Panayotis Kevrekidis 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 chapter 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.