A simple model for estimating the prevalence of HIV-infected persons

Article Abstract:

It is not possible to ascertain directly the exact actual value of prevalence of HIV-infected persons without clinical symptoms of AIDS. Therefore a very simple simulation model was developed for the estimation of this value in the early stage of the epidemic. This model is based on the principles of the general method of multicompartmental models and its core is the so-called one-way transport segment which imitates very faithfully the supposed transition of HIV-infected persons through the stage from the transmission of infection to AIDS manifestation. The number of AIDS cases is represented in the model by a compartment. The essence of the estimation procedure is also very simple - it consists in the finding of such shape of the time-dependent parameter of exponential input function of the transport segment for which the course of the compartment measure values agree with the ascertained or prognosticated data about the numbers of AIDS cases. The dependence of the exponential function parameter on the product of the average probability that the infection is transmitted from the infected to the receptive individual and of the average rate at which new sexual partners are required can be shown. (Reprinted by permission of the publisher.)

Estimation

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Simulation analysis of some basic hypotheses about the spread of AIDS

Article Abstract:

The basic dynamics of the AIDS epidemic in an homogeneous population is studied from three different points of view using simple mathematical models. The first model assumes a constant transmission probability per sexual intercourse and a constant frequency of sexual intercourses. Then the probability for HIV infection strongly increases with increasing number of partners only if the infection probability per intercourse is relatively high. Second, the assumption that each carrier transmits the infection a constant number of times with a constant time interval between transmissions is shown to result in an exponential rise in the number of infected. Taking the saturation effect into account the number of new infections per year and the actual proportion of infected are studied in populations of different sizes. The third model assumes an exponential rise in the number of infected and a randomly distributed incubation time of AIDS. This results in stochastic simulation of the rise in AIDS cases. With repeated simulation runs the stochastic dispersion of the rise is shown to be quite large, obscuring the so-called transient phenomenon in the initial phase of the epidemic. (Reprinted by permission of the publisher.)

Discrete Simulation, Stochastic Model

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Dynamic models of the AIDS epidemic

Article Abstract:

This paper describes HIV transmission models built using STELLA, a new language for the Apple Macintosh. These include a basic model, or template, of sexual transmission of HIV; a model of heterosexual transmission constructed from the template; and a model which simulates transmission caused by needle sharing. This paper also describes a computer program, based on the template rate equations which optimizes key epidemiological parameters associated with the early epidemic in San Francisco. With this program we have shown that the per contact transmission probability (infectivity) of the antigen-positive first stage of infection may be significantly higher than the infectivity of the antibody-positive subsequent stage. This finding stresses the importance of screening for viral antigens to detect first stage infection in high risk groups. (Reprinted by permission of the publisher.)

Medical research, Dynamic Systems, Behavioral Science

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