Optimization of protection of computer networks against malicious software

Many computer viruses cause repeated epidemics of malwares and induce a serious challenge for IT security. IT security needs to apply the countermeasures iteratively during series of epidemic events to stop the propagation process. We consider a modification of Susceptible-Infected-Recovered model with impulses of control and present the model of propagation of two forms of malware. We discuss the motivation for the formulation an impulse control problem that seeks to minimize a number of infected nodes in the network. The total system cost includes the economic value of security risks and resources required by procedures of protection of the network. We show the structure of impulse antivirus policy and represent numerical simulations.