A Self-Organized Method for Computing the Epidemic Threshold in Computer Networks

TL;DR

This work presents a method for getting local information about the infection level (risk perception) in human epidemics without resorting to repeated simulations, and shows that the method can be applied to this case, too.

Abstract

In many cases, tainted information in a computer network can spread in a way similar to an epidemics in the human world. On the other had, information processing paths are often redundant, so a single infection occurrence can be easily "reabsorbed". Randomly checking the information with a central server is equivalent to lowering the infection probability but with a certain cost (for instance processing time), so it is important to quickly evaluate the epidemic threshold for each node. We present a method for getting such information without resorting to repeated simulations. As for human epidemics, the local information about the infection level (risk perception) can be an important factor, and we show that our method can be applied to this case, too. Finally, when the process to be monitored is more complex and includes "disruptive interference", one has to use actual simulations, which however can be carried out "in parallel" for many possible infection probabilities.

Figures (6)

• Figure 1: Evolution of the local minimum value of the percolation parameter $p_i$ for a 1D regular network with $k =2$.
• Figure 2: Asymptotic number of infected individuals $c$ versus the bare infection probability $\tau$ for the SIS dynamics for different networks. From left to right, for $c=0$: Scale Free (SF), Random (Poisson), Regular. Here $N=10000$.
• Figure 3: Critical level $J_c$ for which the infection is stopped, for networks with fixed or peaked connectivity $k = 10$ and $N = 1000$ in the mean-field (MF), regular (RN) and random (RG) case.
• Figure 4: The phase diagram of the Domany-Kinzel cellular automaton model. In the quiescent phase only the state with 0 infected sites is stable. In the active phase the state 0 is unstable and the average number of infected sites is larger than 0. In this phase the long-time evolution only depends on the initial condition, so it may be defined disordered. In the conditionally chaotic and chaotic phase the evolution depends on the initial condition and therefore varies when the configuration is varied (therefore "chaotic"). In the chaotic phase this dependence occurs for all implementations, in the conditionally chaotic one only for some particular computational scheme.
• Figure 5: Left: the average density ($\rho$) as a function of the bare infection probability $\tau$ and in the inset the distribution of the values of $\pi_i$ for which the infection reaches site $i$ (black bar) for the site percolation problem in a regular network with $k=2$ (DK model, $p=q$). Right: the average density ($\rho$) as a function of the bare infection probability $\tau$ and in the inset the distribution of the values of $\pi_i$ for which the infection reaches site $i$ (black bar) for the a "nonlinear" (XOR) percolation problem in a regular network with $k=2$ (DK model $q=0$).