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To improve the accuracy of network-based SIS models we introduce and study a multilayer representation of a time-dependent network. In particular, we assume that individuals have their long-term (permanent) contacts that are always present, identifying in this way the first network layer. A second network layer also exists, where the same set of nodes can be connected by occasional links, created with a given probability. While links of the first layer are permanent, a link of the second layer is only activated with some probability and under the condition that the two nodes, connected by this link, are simultaneously participating to the temporary link. We develop a model for the SIS epidemic on this time-dependent network, analyze equilibrium and stability of the corresponding mean-field equations, and shed some light on the role of the temporal layer on the spreading process.
Networks are a convenient way to represent complex systems of interacting entities. Many networks contain communities of nodes that are more densely connected to each other than to nodes in the rest of the network. In this paper, we investigate the d
Defining an optimal protection strategy against viruses, spam propagation or any other kind of contamination process is an important feature for designing new networks and architectures. In this work, we consider decentralized optimal protection stra
Most real networks are characterized by connectivity patterns that evolve in time following complex, non-Markovian, dynamics. Here we investigate the impact of this ubiquitous feature by studying the Susceptible-Infected-Recovered (SIR) and Susceptib
In this work, we use the spectral properties of graphons to study stability and sensitivity to noise of deterministic SIS epidemics over large networks. We consider the presence of additive noise in a linearized SIS model and we derive a noise index
Stochastic epidemic models on networks are inherently high-dimensional and the resulting exact models are intractable numerically even for modest network sizes. Mean-field models provide an alternative but can only capture average quantities, thus of