Mathematical Modeling of DNA Repeats and HIV Epidemics

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This project applies the research group's expertise in nonlinear dynamics and mathematical modeling to improve the understanding of two extremely important topics: The propagation of HIV infection and origin and dynamics of repetitive structures in genome. There are many unresolved scientific questions about the transmission of the HIV virus, among them the relative infectivity of people at different stages of the disease and the extent to which people can acquire resistance to the virus. A model for HIV transmission among homosexual men has been developed, based on a detailed data set from the onset of the AIDS crisis in San Francisco. By taking into account the widely varying levels of sexual activity in the population, the data can be fit quite well with parameters that imply a higher late stage infectivity than has been commonly believed. A similar model will be developed for heterosexual HIV transmission and to incorporate additional features into these models, such as acquired resistance and the effect of various prevention measures. By comparing these models with additional data sets, infectivity rates for men and women will be estimated, the effect of acquired resistance will be quantified, and the effectiveness of various prevention strategies will be evaluated. Answering the HIV questions described above will have an impact both on public health policy and on the development of new methods for prevention and treatment of HIV. The results will be critical to understanding the value of screening for infected individuals in slowing the epidemic. Another question studied is the "Repetitive DNA", which refers to separate regions of genomes of various species that are very similar to each other. These repetitive regions are important for several reasons: They are a major obstruction to correctly determining the genomic sequence, they provide valuable information about the evolution of the genome, and in all likelihood they have more biological function than is currently understood. Remarkable statistical features of the repetitive regions for several genomes have been discovered. Long repetitive regions and the mechanisms by which these regions are created, destroyed, and mutated over time are of particular interest. A detailed analysis of the differences between the human and chimpanzee genomes will be performed; in some cases, one genome will have an extra (repetitive) copy of a DNA segment that is in both genomes, and in other cases one genome will be missing a segment that is in the other genome. The processes by which these segments are copied and deleted as a species evolves will be modeled.