A spatial stochastic model for worm propagation: scale effects

Realistic models for worm propagation in the Internet have become one of the major topics in the academic literature concerning network security. In this paper, we propose an evolution equation for worm propagation in a very small number of Internet hosts, hereinafter called a subnet and introduce a generalization of the classical epidemic model by including a second order spatial term which models subnet interactions. The corresponding gradient coefficient is a measure of the characteristic scale of interactions and as a result a novel scale approach for understanding the evolution of worm population in different scales, is considered. Results concerning random scan strategies and local preference scan worms are presented. A comparison of the proposed model with simulation results is also presented. Based on our model, more efficient monitoring strategies could be deployed.