Related papers: Limiting Speed and Fluctuations for the Boundary M…
Fluctuation relations imply the second-law inequality $\langle\Sigma_T\rangle\ge0$, but path extrema can also constrain how large the mean entropy production can be. For steady-state processes with entropy-production martingale…
The current work deals with an epidemic model on the complete graph K_n on n vertices in a non-homogeneous setting, where the vertices may have distinct types. Different types differ in the probability of getting infected, and/or in the…
Random walk is one of the basic mechanisms found in many network applications. We study the epidemic spreading dynamics driven by biased random walks on complex networks. In our epidemic model, each time infected nodes constantly spread…
In this paper we are concerned with the SIR (Susceptible-Infective-Removed) epidemic on open clusters of bond percolation on the squared lattice. For the SIR model, a susceptible vertex is infected at rate proportional to the number of…
Epidemic spreading and cascading failure are two important dynamical processes over complex networks. They have been investigated separately for a long history. But in the real world, these two dynamics sometimes may interact with each…
This paper studies a distributed continuous-time bi-virus model in which two competing viruses spread over a network consisting of multiple groups of individuals. Limiting behaviors of the network are characterized by analyzing the…
We consider epidemic extinction in finite networks with broad variation in local connectivity. Generalizing the theory of large fluctuations to random networks with a given degree distribution, we are able to predict the most probable, or…
This paper develops a unified theoretical framework for detecting and estimating boundaries in treatment effects across both spatial and temporal dimensions. We formalize the concept of treatment effect boundaries as structural parameters…
Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the…
Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…
The critical behavior of the contact process in disordered and periodic binary 2d-lattices is investigated numerically by means of Monte Carlo simulations as well as via an analytical approximation and standard mean field theory.…
In this paper we conduct a simulation study of the spread of an epidemic like COVID-19 with temporary immunity on finite spatial and non-spatial network models. In particular, we assume that an epidemic spreads stochastically on a…
A bootstrap percolation process on a graph G is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round every uninfected node which has at least r infected neighbours…
The epidemic process on a graph is considered for which infectious contacts occur at rate which depends on whether a susceptible is infected for the first time or not. We show that the Vasershtein coupling extends if and only if secondary…
We study a contact process on a two-dimensional square lattice which is diluted by randomly removing bonds with probability p. For p<1/2 and varying birth rate $\lambda$ the model was shown to exhibit a continuous phase transition which…
The contact process on dynamic edges (CPDE) is a contact process evolving on a dynamic environment given by a dynamical percolation on the edges of Z d\,: each edge updates its state to open or closed with respective rates vp and v(1 -p).…
We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as…
We study the effects of topological (connectivity) disorder on phase transitions. We identify a broad class of random lattices whose disorder fluctuations decay much faster with increasing length scale than those of generic random systems,…
We consider an interacting particle system on the one dimensional lattice $\bf Z$ modeling combustion. The process depends on two integer parameters $2\le a<M<\infty$. Particles move independently as continuous time simple symmetric random…
We consider the propagation of a contagion process (epidemic) on a network and study the problem of dynamically allocating a fixed curing budget to the nodes of the graph, at each time instant. For bounded degree graphs, we provide a lower…