Abstract
The main purpose of this paper is to give a short account of two mathematical models dealing with the HIV dynamics. Details and proofs of these results are presented in [1], [2], [3], [8]. As well known AIDS epidemics has particularities which made it quite different from previous epidemics. First there are wide variations in human sexual behaviour (heterogeneity both of the individuals and the contacts they make). Secondly the time-lag between infection by HIV and the appearance of overt AIDS is both long and variable (median roughly about 10 years for homosexual men). Thirdly the degree of infectiousness is also time dependent. To include all these facts discrete stochastic models are really necessary and needed. For this reason we have proposed and developed in recent years in Bielefeld a new type of stochastic modelling based on Random Graphs which allows both precise mathematical predictions and better adaptation to the available behavioural, epidemiological and biological data. This model will be presented in Section II.
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