Discrete stochastic model of HIV infection spread within a heterogeneous population

A discrete stochastic model of HIV infection spread within a heterogeneous population is presented. A system of high-dimensional stochastic difference equations is used in the model. A system of upper estimates for mathematical expectations of the sizes of groups of individuals in the population is constructed. Sufficient conditions for the extinction of the infection process are obtained in terms of M-matrices. Based on the Monte Carlo method, a numerical algorithm and a simulation code are developed, which allows one to study probabilistic characteristics of the observed variables of the model. Results of numerical experiments are presented.