Simulation analysis of some basic hypotheses about the spread of AIDS

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.