A Gillespie Algorithm and Upper Bound of Infection Mean on Finite Network

Abstract

Cyber-attacks are expected to increase in the next few years. This condition requires an estimate of the amount of risk that will occur. Cyber risk can be reflected in the number of infected computers obtained by models that can explain the process of spreading viruses on computer networks. Mathematical models on epidemiology can be used to understand the process of spreading viruses on computer networks inspired by the process of spreading diseases in biological populations. Stochastic susceptible-infectious-susceptible (SIS) model is a simple epidemic model will be used to estimate the risk (number of infected computers) on several computer networks. Based on a fixed population and homogeneous mixing assumptions, we get the upper bound of infection mean from the model. Mean of the sample path in dynamic processes is generated by the Gillespie Algorithm or Simulation Stochastic Algorithm (SSA) to compare with the upper bound of the infection mean. The computational result confirms the mean of sample paths always less than the upper bound of infection mean.