A new version of the law of large numbers for an epidemic model

In the review part of the talk the epidemic models proposed by Telcs, Wormald, Popov, Alves, Durrett and others are considered. The main attention is paid to the new epidemic model introduced by the author. This model extends the scheme studied by Machado, Mashurian and Matzinger. Bounds of large deviations probabilities for sums of independent random variables and certain results related to the theory of branching processes play the essential role in the investigation. A nonimprovable version of the law of large numbers is established for the new model. Moreover, zero-one laws for random graphs proved by the author will be tackled as well.
М.Е. Жуковский, Закон больших чисел для моделии эпидемии, Доклады Академии Наук, принято в печать, 2011.