The authors of this paper first analyze recent work on the epidemic spreading of malware in arbitrary networks, noting that all previous studies only considered push-based infection (where infected hosts actively infect neighbors). They extend this research to include pull-based infections, such as drive-by downloads. To this end, they introduce three parameters (α, β, and γ), denoting the probability that a given node (α) suffers a push-based infection, (β) is infected using a pull-based method, or (γ) is cured.

The researchers then describe a general sufficient condition (also called an epidemic threshold) under which the spreading becomes stable, and a more succinct version that holds true under more specific assumptions. They follow with a theorem for upper and lower bounds of the infection rate, “regardless of the stability of the spreading.”

The theorems presented in the previous sections are confirmed using simulations. The paper uses datasets from Epinions, a social network, and “a graph representing Enron’s internal email communications.” Although “both networks exhibit power-law degree distributions,” it should be noted that the theorems apply to arbitrary networks as well.

The authors then discuss the influence of a node’s degree on its infection rate, formulating an approximating equation in which the degree is a nonlinear factor and confirming it via simulation.

Furthermore, they examine whether “the mean field approach is applicable in arbitrary networks.” This approach is a statistical method in which random variables are replaced with their expected (mean) values. The authors argue that this procedure is indeed viable under the condition that the probability of a push-based infection is very small.

Lastly, the authors show that the global mean infection rate can be accurately approximated by monitoring only a small constant number of nodes with average degrees and certain second-order degrees.

The target audience for this paper includes graduate students and researchers with a theoretical background in computer science or mathematics. The formalization makes it hard reading for practitioners; simply put, there are lots of formulas.