For explanation and prediction of the evolution of infectious diseases in populations, researchers often use simplified mathematical models for simulation. We believe that the results from these models are often questionable when the epidemic dynamics becomes more complex, and that developing more realistic models is intractable. In this dissertation we propose to simulate infectious disease propagation using dynamic and complex networks. We present the Simulator of Epidemic Evolution using Complex Networks (SEECN), an expressive and high-performance framework that combines algorithms for graph generation and various operators for modeling temporal dynamics. For graph generation we use the Kronecker algorithm, derive its underlying statistical structure and exploit it for a variety of purposes. Then the epidemic is evolved over the network by simulating the dynamics of the population and the epidemic simultaneously, where each type of dynamics is performed by a separate operator. All dynamics operators can be fully and independently parameterized, facilitating incremental model development and enabling different influences to be toggled for differential analysis. As a prototype, we simulate two relatively complex models for the HIV epidemic and find a remarkable fit to reported data for AIDS incidence and prevalence. Our most important conclusion is that the mere dynamics of the HIV epidemic is sufficient to produce rather complex trends in the incidence and prevalence statistics, e.g. without the introduction of particularly effective treatments at specific times. We show that this invalidates assumptions and conclusions made previously in the literature, and argue that simulations used for explanation and prediction of trends should incorporate more realistic models for both the population and the epidemic than is currently done. In addition, we substantiate a previously predicted paradox that the availability of Highly Active Anti-Retroviral Treatment likely causes an increased HIV incidence.