  Modeling spreading processes in complex random networks plays an essential
role in understanding and prediction of many real phenomena like epidemics or
rumor spreading. The dynamics of such systems may be represented
algorithmically by Monte-Carlo simulations on graphs or by ordinary
differential equations (ODEs). Despite many results in the area of network
modeling the selection of the best computational representation of the model
dynamics remains a challenge. While a closed form description is often
straightforward to derive, it generally cannot be solved analytically; as a
consequence the network dynamics requires a numerical solution of the ODEs or a
direct Monte-Carlo simulation on the networks. Moreover, Monte-Carlo
simulations and ODE solutions are not equivalent since ODEs produce a
deterministic solution while Monte-Carlo simulations are stochastic by nature.
Despite some recent advantages in Monte-Carlo simulations, particularly in the
flexibility of implementation, the computational cost of an ODE solution is
much lower and supports accurate and detailed output analysis such as
uncertainty or sensitivity analyses, parameter identification etc. In this
paper we propose a novel approach to model spreading processes in complex
random heterogeneous networks using systems of nonlinear ordinary differential
equations. We successfully apply this approach to predict the dynamics of
HIV-AIDS spreading in sexual networks, and compare it to historical data.
