Mathematical Modeling of DNA Repeats and HIV Epidemics

这个项目应用了研究小组在非线性动力学和数学建模方面的专业知识，以提高对两个极其重要的主题的理解：艾滋病毒感染的传播和基因组中重复结构的起源和动力学。关于艾滋病毒的传播，有许多科学问题尚未解决，其中包括处于疾病不同阶段的人的相对传染性，以及人们对病毒的抵抗力程度。根据旧金山艾滋病危机爆发以来的一组详细数据，开发了一个同性恋男性中艾滋病毒传播的模型。通过考虑人群中差异很大的性活动水平，数据可以很好地与参数相吻合，这些参数意味着晚期传染性比通常认为的更高。将为异性恋艾滋病毒传播开发一个类似的模型，并在这些模型中纳入其他特征，如获得性抵抗力和各种预防措施的效果。通过将这些模型与其他数据集进行比较，将估计男性和女性的传染性比率，将量化获得性耐药性的影响，并将评估各种预防策略的有效性。回答上述艾滋病毒问题将对公共卫生政策和制定预防和治疗艾滋病毒的新方法产生影响。这一结果将对理解筛查感染者在减缓疫情方面的价值至关重要。另一个被研究的问题是“重复DNA”，它指的是不同物种基因组中彼此非常相似的独立区域。这些重复区域之所以重要，有几个原因：它们是正确确定基因组序列的主要障碍，它们提供了关于基因组进化的有价值的信息，它们很可能具有比目前了解的更多的生物学功能。发现了几个基因组重复区的显著统计特征。人们特别感兴趣的是长时间的重复区域以及这些区域随着时间的推移而被创建、销毁和突变的机制。将对人类和黑猩猩基因组之间的差异进行详细分析；在某些情况下，一个基因组将具有两个基因组中DNA片段的额外(重复)副本，而在其他情况下，一个基因组将丢失另一个基因组中的一个片段。随着物种的进化，这些片段被复制和删除的过程将被建模。

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.