Virus dynamics and control in computer networks

Description

For long time researchers have been aiming at quantitative tools for understanding the fundamentals of virus propagation [R1]. Since these early attempts, mathematical epidemiological models have matured to a solid branch of mathematics, giving raise to an extensive literature on the topic [R2] and finding applications in epidemiology and other sciences. Following up research in virus spreading in human and animal communities, researchers have been proposing the use of mathematical models of viruses also in computer networks [R3], with the purpose of having a reliable analytical set-up for research on viruses in data networks without requiring in-vivo experiments.

Since its introduction in the ‘20s [R4,R5], the SIR model and its variations have represented some of the most adopted models for epidemiological studies. The SIR model describes the evolution of the proportion of Susceptible, Infected and Removed (or Recovered) individuals in a community. One of its variations, the so-called SIR model without vital dynamics, has also attracted interest in the data network community [R6] and extended to a compartmental-based model to include the case of data sub-networks interconnected over a larger network. Other modelling approaches based on a mean-field approximation of a continuous-time Markov model [R7] lead to comparable models.

Analytical studies on the networked SIR model proposed recently [R8,R9] have focused on characterizing values of the parameters of the SIR model under which the infection comes to an end with a prescribed velocity of convergence while minimizing a cost function. These studies are motivated by the possibility of reducing the virus spreading by acting on control parameters such as cure rates and immunization. In models of computer networks supported by experimental validation, however, these parameters are fixed (and actually matched to reproduce the time behaviour of the virus spreading measured “in vivo”) and characteristic of the virus dynamics. As a consequence, other control approaches have been considered. In [R10], it has been proposed to counteract the effect of virus spread by countermeasures (patches), GSS Training and Supervision Plan - Scholarship PhD student - 3 - which are diffused in the network following a virus-like dynamics. From a control-theoretic point of view the latter approach is a remarkable example of dynamic (vs. static) closed-loop (vs. open-loop) virus control. Although the approach of [R10] has been proposed to model the outbreak of a particular worm (Code Red worm), the principle can inspire several other active control strategies.