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Center for Nonlinear Studies |
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 viral growth and random accumulation of mutations. We analyze the Hamming distance (HD) distribution among viral sequences assuming either synchronous or asynchronous infection of cells in the absence of selection and recombination, and show how we implement this theoretical framework into the webtool "Poisson Fitter," which is available on the LANL HIV database. In the second half of the talk, we introduce recombination and develop a combinatorial approach to estimate the change in the HD distribution. We also describe a continuous and completely random generalization of the model and show that under more complicated scenarios the mean HD still grows linearly with time, thus validating our original, simpler model. We conclude with a brief description of the RV 217 ECHO cohort, which is currently enrolling uninfected, high-risk patients from Africa and Thailand and, because of the frequency at which subjects are sampled, will be ideal for our proposed analysis.