Computer viruses are major threats to Internet security and privacy, therefore many researchers are addressing questions linked to virus propagation properties, spreading models, epidemic dynamics, tipping points, and control strategies. We believe that two important factors – resource limitations and costs – are being overlooked in this area due to an overemphasis on power-law connectivity distributions of scale-free networks affecting computer virus epidemic dynamics and tipping points. The study show (a) a significant epidemic tipping point does exists when resource limitations and costs are considered, with the tipping point exhibiting a lower bound; (b) when interaction costs increase or usable resources decrease, epidemic tipping points in scale-free networks grow linearly while density curves decrease linearly; (c) regardless of whether Internet user resources obey delta, uniform, or normal distributions, they retain the same epidemic dynamics and tipping points as long as the average value of those resources remains unchanged across different scale-free networks; (d) it is possible to control the spread of a computer virus in a scale-free network if resources are restricted and if costs associated with infection events are significantly increased through the use of a throttling strategy. The proposed model shows how resource and costs influence the epidemic dynamics of computer viruses in scale-free networks. A significant tipping point does exists on the epidemic dynamics of computer viruses when resource and costs are considered. It is possible to control the spread of a computer virus if resources are restricted and if costs significantly increased.