Date of Award
Doctor of Philosophy (PhD)
growth model, Hamming distance, HIV infection, population genetics, Viral dynamics
Mathematics | Statistics and Probability
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.
Giorgi, Elena Edi, "A Mathematical Growth Model of the Viral Population in Early HIV-1 Infections" (2011). Open Access Dissertations. Paper 458.