Discrete-time moment closure models for epidemic spreading in populations of interacting individuals

AbstractUnderstanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible–infectious–removed) dynamics propagated on contact networks. We derive a novel set of ‘discrete-time moment equations’ for the probability of the system states at the level of individual nodes and pairs of nodes. These equations form a set which we close by introducing appropriate approximations of the joint probabilities appearing in them. For the example case of SIR processes, we formulate two types of model, one assuming statistical independence at the level of individuals and one at the level of pairs. From the pair-based model we then derive a model at the level of the population which captures the behavior of epidemics on homogeneous random networks. With respect to their continuous-time counterparts, the models include a larger number of possible transitions from one state to another and joint probabilities with a larger number of individuals. The approach is validated through numerical simulation over different network topologies

Multiple Hysteresis Jump Resonance in a Class of Forced Nonlinear Circuits and Systems

In this paper, a new class of systems with nonclassical jump resonance behavior is presented. Although jump resonance has been widely studied in the literature, this contribution refers to systems presenting a multiple hysteresis jump resonance phenomenon, meaning that the frequency response of the system presents more hysteresis windows nested within the same range of frequency. The analytical conditions for observing this type of behavior are derived and a design strategy to obtain multiple hysteresis jump resonance in circuits and systems presented

Hubs-attracting laplacian and related synchronization on networks

In this work, we introduce a new Laplacian matrix, referred to as the hubs-attracting Laplacian, accounting for diffusion processes on networks where the hopping of a particle occurs with higher probability from low to high degree nodes. This notion complements the one of the hubs-repelling Laplacian discussed in [E. Estrada, Linear Algebra Appl., 596 (2020), pp. 256-280], that considers the opposite scenario, with higher hopping probabilities from high to low degree nodes. We formulate a model of oscillators coupled through the new Laplacian and study the synchronizability of the network through the analysis of the spectrum of the Laplacian. We discuss analytical results providing bounds for the quantities of interest for synchronization and computational results showing that the hubs-attracting Laplacian generally has better synchronizability properties when compared to the classical one, with a low occurrence rate for the graphs where this is not true. Finally, two illustrative case studies of synchronization through the hubs-attracting Laplacian are considered

Application of the Complex Network Theory in Urban Environments. A Case Study in Catania

Abstract Cities are responsible for the 70% of the world's energy demand and represent the largest source of GHG emissions. The constant growth of cities encourages towards the configuration of urban energy plans in order to make urban areas more sustainable places. In this direction, Decentralized Energy Systems (DES) play an important role in order to improve the efficiency in urban energy consumptions. However, the decentralization of urban energy systems requires a comprehensive evaluation of the energy interactions that can occur among consumers. To this aim, proper mathematical models need to be defined in order to take into account how those interactions occur. In this paper, a mathematical procedure based on the complex network theory is introduced and tested to a neighborhood within the city of Catania

Robustness of Synchronization to Additive Noise: How Vulnerability Depends on Dynamics

From biological to technological networks, scientists and engineers must face the question of vulnerability to understand evolutionary processes or design-resilient systems. Here, we examine the vulnerability of a network of coupled dynamical units to failure or malfunction of one of its nodes. More specifically, we study the effect of additive noise that is injected at one of the network sites on the overall synchronization of the coupled dynamical systems. In the context of mean square stochastic stability, we present a mathematically principled approach to illuminate the interplay between dynamics and topology on network robustness. Through the new theoretical construct of robust metric, we uncover a complex and often counterintuitive effect of dynamics. While networks are more robust to noise injected at their hubs for a classical consensus problem, these hubs could become the most vulnerable nodes for higher order dynamics, such as second-order consensus and Rossler chaos. From the exact treatment of star networks and the systematic application of perturbation techniques, we offer a mechanistic explanation of these surprising results and lay the foundation for a theory of dynamic robustness of networks