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.
