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Modeling spreading processes in complex random networks plays an essentialrole in understanding and prediction of many real phenomena like epidemics orrumor spreading. The dynamics of such systems may be representedalgorithmically by Monte-Carlo simulations on graphs or by ordinarydifferential equations (ODEs). Despite many results in the area of networkmodeling the selection of the best computational representation of the modeldynamics remains a challenge. While a closed form description is oftenstraightforward to derive, it generally cannot be solved analytically; as aconsequence the network dynamics requires a numerical solution of the ODEs or adirect Monte-Carlo simulation on the networks. Moreover, Monte-Carlosimulations and ODE solutions are not equivalent since ODEs produce adeterministic solution while Monte-Carlo simulations are stochastic by nature.Despite some recent advantages in Monte-Carlo simulations, particularly in theflexibility of implementation, the computational cost of an ODE solution ismuch lower and supports accurate and detailed output analysis such asuncertainty or sensitivity analyses, parameter identification etc. In thispaper we propose a novel approach to model spreading processes in complexrandom heterogeneous networks using systems of nonlinear ordinary differentialequations. We successfully apply this approach to predict the dynamics ofHIV-AIDS spreading in sexual networks, and compare it to historical data.

Continuous Models of Epidemic Spreading in Heterogeneous Dynamically Changing Random Networks