Long & Medium Term Research: Mathematical Modeling of Pair Formation and Fertility in an HIV Infected Population

长期中期研究：配对的数学建模 HIV感染人群的形成和生育力 该奖项是根据长期计划提出的。 &在国外卓越中心的中期研究。 的 该计划旨在使美国科学家和工程师能够 在国外的研究机构进行长期研究， 证明卓越。 奖项提供了机会， 开展联合研究，以及使用独特或复杂的 实验设施、专业知识和实验条件 国外 该奖项将支持玛格丽特博士为期18个月的访问 美国马萨诸塞州/阿默斯特大学校长 联合王国，与Roy M.安德森在 伦敦帝国理工学院 伦敦关于“电子对形成的数学模型和 艾滋病毒感染人群的生育率。“艾滋病的流行 为人类种群生物学增添了新的维度， 在择偶和繁殖中固有的行为是 正是病毒传播的条件 导致艾滋病。 这项研究将探讨交配结构如何 与生育率有关的艾滋病毒感染者， 一个数学模型和计算机模拟，并会问： (1)什么样的交配行为最大化生育能力， 感染的风险？（2）死亡率如何与 艾滋病影响个人满足文化的能力 明确的交配偏好 该模型将定义一个配对 功能依赖于交配所指，这将是 定义为配对的概率分布， 依赖其所属类别的个人 由配合结构限定。 建立的变量 交配结构反映了感染的风险结构 包括年龄、居住地、感染或易感状态， 性行为课 男性和女性人口 可以表示为向量，再细分为 变量 矩阵的内容由 亚部之间成对形成的速率。 由于这些 价值观是产品，系统是非线性的，标准的 不能使用迭代过程。 拟牛顿法 将被用来寻找解决方案， 技术，以寻找最大限度地提高生育率的价值， 最大限度地降低感染风险。 一系列的计算机模拟 将改变分配给概率分布的值 定义交配参照物，并改变传播假设 艾滋病导致的死亡率、生育率、性活动和道德。 授标建议提供资金， 适当的，国际旅行，出国当地旅行， 津贴，家属津贴（如适用）和公寓 美国本土机构的行政津贴为250美元。

Long & Medium-Term Research: Mathematical Modeling of Pair Formation and Fertility in an HIV Infected Population This award recommendation is made under the Program for Long & Medium-Term Research at Foreign Centers of Excellence. The program seeks to enable U.S. scientists and engineers to conduct long-term research abroad at research institutions of proven excellence. Awards provide opportunities for the conduct of joint research, and the use of unique or compli- mentary facilities, expertise and experimental conditions in foreign countries. This award will support a 18 month visit by Dr. Margaret Gradie of the University of Massachusetts/Amherst to the United Kingdom, to work with Professor Roy M. Anderson at the Imperial College of Science, Technology and Medicine in London on "Mathematical Modeling of Pair Formation and Fertility in an HIV Infected Population." The AIDS epidemic adds a new dimension to human population biology as the behaviors inherent in mate selection and reproduction are precisely the conditions for transmission of the virus causing AIDS. This research will explore how mating structure and fertility relate in an HIV infected population by use of a mathematical model and computer simulation, and will ask: (1) What mating behaviors maximize fertility while minimizing risk of infection?; and (2) How will mortality associated with AIDS affect the ability of individuals to meet culturally defined mating preferences? The model will define a pairing function dependent on the mating referent, which will be defined as a probability distribution of pairing between individuals dependent on their membership in categories defined by the mating structure. The variables which establish the mating structure reflect the risk structure of infection and include age, residence, infected or susceptible status, and sexual activity class. The populations of males and females can be represented as vectors, subdivided by the structure variables. The contents of the matrix are defined by the rates of pair formation between subdivisions. Since these values are products, the system is non-linear, and standard iterative procedures cannot be used. Quasi-Newton methods will be used to look for solutions, and steepest descent techniques to look for values which maximize fertility while minimizing risk of infection. A series of computer simulations will vary the values assigned to the probability distributions defining mating referents, and vary assumptions on transmission rates, fertility, sexual activity, and morality due to AIDS. The award recommendation provides funds to cover, as appropriate, international travel, local travel abroad, stipend, dependents' allowance if applicable, and a flat administrative allowance of $250 for the U.S. home institution.