Whether or not a critical threshold exists when epidemic diseases are spread in complex networks is a problem attracting attention from researchers in several disciplines. In 2001, Pastor-Satorras and Vespignani used a computational simulations approach to show that epidemic diseases which spread through scale-free social networks do not have positive critical thresholds. In other words, even if a disease has almost no chance of being transmitted from one person to another, it can still spread throughout a scale-free network. However, they ignored two key factors that have a large impact on epidemic dynamics: economic resource limitations and transmission costs. Every infection event entails tangible or intangible costs in terms of time, energy, or money to the carrier, recipient, or both. Here we apply an agent-based modeling and network-oriented computer simulation approach to analyze the influences of resource limitations and transmission costs on epidemic dynamics and critical thresholds in scale-free networks. Our results indicate that when those resources and costs are taken into consideration, the epidemic dynamics of scale-free networks are very similar to those of homogeneous networks, including the presence of significant critical thresholds. It is hoped that our data will help epidemiologists, public health professionals, and computer scientists working with core questions of epidemic diseases, estimates of epidemic dynamics and spreading, and effective public health policies and immunization strategies.