This is a collection of state-of-the-art reviews and original research work dealing with statistical and mathematical methodology relevant to the AIDS epidemic. It will be of interest and practical application to researchers and students in statistics, epidemology and public health.

AIDS epidemiology : methodological issues

Age-structured population models and their numerical solution

We propose algorithms for the approximation of the age distributions of populations modeled by the McKendrick-von Foerster and the Gurtin-MacCamy systems both in one- and two-sex versions. For the one-sex model methods of second and fourth order are proposed. For the two-sex model a second order method is described. In each case the convergence is demonstrated. Several numerical examples are given.

Rapidly converging numerical algorithms for models of population dynamics.

The standard model for pair formation is generalized to include a maturation period. This model in the form of three coupled delay equations is a special case of the general age-structured model for a two-sex population. The exact conditions for the existence of an exponential (persistent) two-sex solution are derived. It is shown that this solution is unique and locally stable. In order to achieve these results the theory of homogeneous differential equations is extended to a class of homogeneous delay equations.

Pair formation models with maturation period

On the approximation of the Lotka-McKendrick equation with finite life-span

An explicit finite difference algorithm is developed to approximate the solution of a nonlinear and nonlocal system of integro-differential equations that models the dynamics of a two-sex population. The algorithm is unconditionally stable. The optimal rate of convergence of the algorithm is demonstrated for the maximum norm. Results from a numerical simulation of U.S. population growth from 1970 to 1980 are presented; these compare favorably with the actual data. (EXCERPT)

A finite difference method for a two-sex model of population dynamics

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A finite difference method for a two-sex model of population dynamics