Virus spread in complete bi-partite graphs

Abstract

In this paper we study the spread of viruses on the complete bi-partite graph KM;N . Using mean …eld theory we …rst show that the epidemic threshold for this type of graph sati…es c = 1 p M N , hence, con…rming previous results from literature. Next, we …nd an expression for the average number of infected nodes in the steady state. In addition, our model is improved by the introduction of infection delay. We validate our models by means of simulations. Inspired by simulation results, we analyze the probability distribution of the number of infected nodes in the steady state for the case without infection delay. The mathematical model we obtain is able to predict the probability distribution very well, in particular, for large values of the e¤ective spreading rate. It is also shown that the probabilistic analysis and the mean …eld theory predict the same average number of infected nodes in the steady state. Finally, we present a heuristic for the prediction of the extinction probability in the …rst phase of the infection. Simulations show that, for the case without infection delay, this time dependent heuristic is quite accurate.

A privacy-restoring mechanism for offline RFID systems

“…In this vein, we showed that our protocol can also be used to spread other kinds of information within the system. tion of viruses on a complete bipartite graph [32]. Their mathematical model is able to predict the probability of spread accurately.…”