相关论文: Comparison of mean-field based theoretical analysi…
Two versions of the susceptible-infected-susceptible epidemic model, which have different transmission rules, are analysed. Both models are considered on a weighted network to simulate a mitigation in the connection between the individuals.…
Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the…
Epidemic propagation on networks represents an important departure from traditional massaction models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using…
We study the properties of the potential overlap between two networks $A,B$ sharing the same set of $N$ nodes (a two-layer network) whose respective degree distributions $p_A(k), p_B(k)$ are given. Defining the overlap coefficient $\alpha$…
We review and refine the concept of a mean-field theory for the study of sandpile models, which are of central importance in the study of self-organized criticality. By considering the simple one-dimensional random walker with an absorbing…
Mean field theory models of percolation on networks provide analytic estimates of network robustness under node or edge removal. We introduce a new mean field theory model based on generating functions that includes information about the…
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to…
Understanding capabilities and limitations of different network architectures is of fundamental importance to machine learning. Bayesian inference on Gaussian processes has proven to be a viable approach for studying recurrent and deep…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is comprised of a system of ordinary differential equations…
Although viral spreading processes taking place in networks are often analyzed using Markovian models in which both the transmission and the recovery times follow exponential distributions, empirical studies show that, in many real…
Metapopulation models provide the theoretical framework for describing disease spread between different populations connected by a network. In particular, these models are at the basis of most simulations of pandemic spread. They are…
In this paper, we propose and analyze a reaction-diffusion susceptible-infected-susceptible (SIS) epidemic patch model. The individuals are assumed to reside in different patches, where they are able to move inside and among the patches.…
Epidemic threshold is one of the most important features of the epidemic dynamics. Through a lot of numerical simulations in classic Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Susceptible (SIS) models on various types of…
We study the standard SIS model of epidemic spreading on networks where individuals have a fluctuating number of connections around a preferred degree $\kappa $. Using very simple rules for forming such preferred degree networks, we find…
The susceptible-infected-recovered (SIR) model has been used extensively to model disease spread and other processes. Despite the widespread usage of this ordinary differential equation (ODE) based model which represents the mean-field…
It is common to use a compartmental, fluid model described by a system of ordinary differential equations (ODEs) to model disease spread. In addition to their simplicity, these models are also the mean-field approximations of more accurate…
Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach…
Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural…
In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…