Related papers: Limiting Speed and Fluctuations for the Boundary M…
We study the spreading speed of a diffusive epidemic model proposed by Li et al. \cite{LL}, where the Stefan boundary condition is imposed at the right boundary, and the left boundary is subject to the homogeneous Dirichlet and Neumann…
We investigate a non-Markovian analogue of the Harris contact process in a finite connected graph G=(V,E): an individual is attached to each site x in V, and it can be infected or healthy; the infection propagates to healthy neighbors just…
In this article, we study an interacting particle system in the context of epidemiology where the individuals (particles) are characterized by their position and infection state. We begin with a description at the microscopic level where…
We study a generalization of the classical contact process (SIS epidemic model) in a directed graph $G$. Our model is a continuous-time interacting particle system in which at every time, each vertex is either healthy or infected, and each…
The contact process, or SIS epidemic, is a continuous-time Markov process used to model the spread of infection on a graph. Each vertex is either healthy or infected, and each infected vertex independently infects each of its healthy…
In the present paper, we study the relation between criticality and information transmission in the one-dimensional contact process with infection parameter $\lambda .$ To do this we define the {\it sensitivity} of the process to its…
If we consider the contact process with infection rate $\lambda$ on a random graph on $n$ vertices with power law degree distributions, mean field calculations suggest that the critical value $\lambda_c$ of the infection rate is positive if…
We consider the contact process on finite and connected graphs and study the behavior of the extinction time, that is, the amount of time that it takes for the infection to disappear in the process started from full occupancy. We prove,…
In this paper we introduce a contact process on a dynamical long range percolation (CPDLP) defined on a complete graph $(V,\mathcal{E})$. A dynamical long range percolation is a Feller process defined on the edge set $\mathcal{E}$, which…
The mathematical model of the spread of the epidemic is developed, which considers fluctuations in the number of human social contacts. The model is based on the logistic equation. The oscillation in the number of social contacts within one…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma}$. We study the dynamical behavior of the…
We study probabilities of various rare events for the limiting point process that appears at the random matrix hard edge. We also show a transition from hard edge to bulk behavior. Asymptotic events studied include a central limit theorem…
We study critical spreading dynamics in the two-dimensional contact process (CP) with quenched disorder in the form of random dilution. In the pure model, spreading from a single particle at the critical point $\lambda_c$ is characterized…
We consider a supercritical catalytic branching random walk (CBRW) on a multidimensional lattice Z^d (d is positive integer). The main subject of study is the behavior of particles cloud in space and time. For CBRW on an integer line,…
Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed in the physics literature, the so-called contact process (CP) where the contagion is expanded at…
The three state contact process is the modification of the contact process at rate $\mu$ in which first infections occur at rate $\lambda$ instead. Chapters 2 and 3 consider the three state contact process on (graphs that have as set of…
In the multitype contact process, vertices of a graph can be empty or occupied by a type 1 or a type 2 individual; an individual of type $i$ dies with rate 1 and sends a descendant to a neighboring empty site with rate $\lambda_i$. We study…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
In this paper, we prove lower and upper bounds for the extinction time of the contact process on random geometric graphs with connecting radius tending to infinity. We obtain that for any infection rate $\lambda >0$, the contact process on…