Related papers: SIS epidemics on open networks: A replacement-base…
Consider a migration process based on a closed network of N stations with K_N customers. Each station is a ./M/\infty queue with service (migration) rate mu. Upon departure, a customer is routed at random to another station. In addition to…
Dynamical systems running on the top of complex networks has been extensively investigated for decades. But this topic still remains among the most relevant issues in complex network theory due to its range of applicability. The contact…
Starting from a stochastic individual-based description of an SIS epidemic spreading on a random network, we study the dynamics when the size $n$ of the network tends to infinity. We recover in the limit an infinite-dimensional…
We explore a rigorous formulation of agent-based SIR epidemic dynamics as a discrete-state Markov process, capturing the stochastic propagation of infection or an invading agent on networks. Using indicator functions and corresponding…
We propose a mathematical model to study coupled epidemic and opinion dynamics in a network of communities. Our model captures SIS epidemic dynamics whose evolution is dependent on the opinions of the communities toward the epidemic, and…
Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…
Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading,…
In this paper, we study the dynamics of contagious spreading processes taking place in complex contact networks. We specifically present a lower-bound on the decay rate of the number of nodes infected by a susceptible-infected-susceptible…
Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place…
We investigate the sensitivity of epidemic behavior to a bounded susceptibility constraint -- susceptible nodes are infected by their neighbors via the regular SI/SIS dynamics, but subject to a cap on the infection rate. Such a constraint…
We present and analyze a mathematical model to study the feedback between behavior and epidemic spread in a population that is actively assessing and reacting to risk of infection. In our model, a population dynamically forms an opinion…
Network epidemics is a ubiquitous model that can represent different phenomena and finds applications in various domains. Among its various characteristics, a fundamental question concerns the time when an epidemic stops propagating. We…
We investigate saturation effects in susceptible-infected-susceptible (SIS) models of the spread of epidemics in heterogeneous populations. The structure of interactions in the population is represented by networks with connectivity…
For a two-dimensional system of agents modeled by molecular dynamics, we simulate epidemics spreading, which was recently studied on complex networks. Our resulting network model is time-evolving. We study the transitions to spreading as…
This paper introduces a new asymptotic regime for simplifying stochastic models having non-stationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the…
Self-adaptive dynamics occurs in many physical systems such as socio-economics, neuroscience, or biophysics. We formalize a self-adaptive modeling approach, where adaptation takes place within a set of strategies based on the history of the…
Over the years numerous models of SIS (susceptible - infected - susceptible) disease dynamics unfolding on networks have been proposed. Here, we discuss the links between many of these models and how they can be viewed as more general…
This paper is focused on SIS (Susceptible-Infected-Susceptible) epidemic dynamics (also known as the contact process) on populations modelled by homogeneous Poisson point processes of the Euclidean plane, where the infection rate of a…
Disease awareness in epidemiology can be modelled with adaptive contact networks, where the interplay of disease dynamics and network alteration often adds new phases to the standard models (Gross et al. 2006, Shaw et al. 2008) and, in…
We investigate the evolution of epidemics over dynamical networks when nodes choose to interact with others in a selfish and decentralized manner. Specifically, we analyze the susceptible-asymptomatic-infected-recovered (SAIR) epidemic in…