Dynamic parameter branching process model of worm propagation

Enormous adverse impacts of Internet worms have attracted strong interest from the academia to model their propagation. This paper presents a dynamic parameter branching process to characterize the spread of scanning worm on the Internet. Firstly, the paper demonstrates that the spread of scanning worm is a typical branching process with dynamic parameters rather than a static parameter. Secondly, by analyzing the influential factors, the paper quantifies dynamic parameters during the propagation. Finally, an explicit expression of the expectation and the probability distribution of the total infected number is proposed. Simulation test verifies the expectation matches the statistics much better than previous models, and the probability distribution explains the deviation between models and statistics. Combining of both the determinism and the randomness, the dynamic parameter branching process model illustrates the essence of the worm propagation.