a b s t r a c tWe study the spreading of contagious diseases in a population of constant size using susceptible-infectiverecovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R 0 ) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R 0 cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations.

Abstract:To investigate the use of classical epidemiological models for studying computer virus propagation we described analogies between computer and population disease propagation using SIR (Susceptible-Infected-Removed) epidemiological models. By modifying these models with the introduction of anti-viral individuals we analyzed the stability of the disease free equilibrium points. Consequently, the basal virus reproduction rate gives some theoretical hints about how to avoid infections in a computer network. Numerical simulations show the dynamics of the process for several parameter values giving the number of infected machines as a function of time.

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