Biomedical subjects

S Yakowitz

Publications and source records attributed to S Yakowitz.

3 recordsLinked to original sources

PubMed1996

Computing marginal expectations for large compartmentalized models with application to AIDS evolution in a prison system.

The customary models for the AIDS epidemic are compartmentalized according to criteria such as risk factors, sexual habits, gender, race, age, and HIV status and stage. Hitherto, with very few exceptions, investigators have resorted to deterministic approximations or to simulation for the computational investigation of such models, which do not yield to purely analytic methods. The present paper describes a numerical technique, not dependent on Monte Carlo simulations, for such compartmentalized Markov population processes. Analytic error bounds and computational evidence suggest that this technique is quite accurate. The study is motivated and illustrated by a model for a prison system, with ten interrelated prisons, twenty compartments, and thousands of individuals. This model is of increasing interest in itself because the HIV/AIDS epidemic is particularly virulent among prison populations, where the environment offers special opportunities to investigate various prevention and educational programmes quantitatively. Our computational techniques are shown to be effective for the analysis of such a prison system, even though the resulting Markov process is an order of magnitude more complicated than other stochastic epidemic models currently being investigated. The modelling approach and numerical device appear to be applicable to a wide variety of population processes involving migration between population patches.

Acquired Immunodeficiency Syndrome↗

PubMed1995

Computational methods for Markov series with large state spaces, with application to AIDS modeling.

AIDS models, and epidemiological models generally, are almost exclusively either differential equations or Markov processes. Of course, the phenomena are fundamentally random, so at best differential equations track the expectation of the process and variability is masked. There are few techniques in the literature for numerical analysis of Markov chains of any size, and so those wishing to analyze stochastic epidemics presently have little alternative to simulation. The contribution of the present paper is to propose numerical techniques capable of finding marginal probabilities of Markov chains having thousands and even millions of states. The ideas are illustrated by application to AIDS models in the literature which formerly had been investigated only through Monte Carlo. This introductory foray has not plumbed the depths of the computational methodology, which yet needs refinement and streamlining that comes through experience. Yet in its primitive form, it is shown herein to be adequate for a computation on the scale of a two-population partition of the San Francisco homosexual epidemic. The closing discussion compares the strengths and weaknesses of the present numerical techniques with the simulation approach to investigation of Markov epidemics.

Acquired Immunodeficiency Syndrome↗

PubMed1993

Modelling the spread of HIV among intravenous drug users.

This paper considers a random allocation model for the transmission of HIV by needle sharing among a group of intravenous drug users who are friends or relatives (buddy-users). A Markov chain approach is used to track the increase in infectives in a stable group of such IVDUs, some of whom are HIV positive. The model is modified to allow for the replacement of infectives in the group, with the group size remaining constant. Further problems are suggested.

HIV Infections↗