Related papers: Contact process on a graph with communities
Most real-world networks are not isolated. In order to function fully, they are interconnected with other networks, and this interconnection influences their dynamic processes. For example, when the spread of a disease involves two species,…
We study a one-dimensional contact process with two infection parameters, one giving the infection rates at the boundaries of a finite infected region and the other one the rates within that region. We prove that the critical value of each…
We study the extinction of epidemics in a generalized susceptible-infected-susceptible model, where a susceptible individual becomes infected with the rate $\lambda$ when contacting $m$ infective individual(s) simultaneously, and an…
In this article, we proposed a susceptible-infected model with identical infectivity, in which, at every time step, each node can only contact a constant number of neighbors. We implemented this model on scale-free networks, and found that…
We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge…
Emergence of new diseases and elimination of existing diseases is a key public health issue. In mathematical models of epidemics, such phenomena involve the process of infections and recoveries passing through a critical threshold where the…
We introduce a Reed-Frost epidemic model with recursive contact tracing and asymptomatic transmission. This generalizes the branching-process model introduced by the authors in a previous work [arxiv:2004.07237] to finite populations and…
Many dynamic processes on complex networks, from disease outbreaks to cascading failures, can rapidly accelerate once a critical threshold is exceeded, potentially leading to severe social and economic costs. Therefore, in order to develop…
The ability to directly record human face-to-face interactions increasingly enables the development of detailed data-driven models for the spread of directly transmitted infectious diseases at the scale of individuals. Complete coverage of…
Traditional disease transmission models assume that the infectious period is exponentially distributed with a recovery rate fixed in time and across individuals. This assumption provides analytical and computational advantages, however it…
We study numerically how the structures of distinct networks influence the epidemic dynamics in contact process. We first find that the variability difference between homogeneous and heterogeneous networks is very narrow, although the…
Understanding how epidemics spread in a system is a crucial step to prevent and control outbreaks, with broad implications on the system's functioning, health, and associated costs. This can be achieved by identifying the elements at higher…
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…
The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action Susceptible-Infected-Recovered model of Kermack and McKendrick. Its usefulness derives largely from its conceptual and mathematical…
Infectious or contagious diseases can be transmitted from one person to another through social contact networks. In today's interconnected global society, such contagion processes can cause global public health hazards, as exemplified by…
We investigate the SIR epidemic on a dynamic inhomogeneous Erd\H{o}s-R\'enyi random graph, in which vertices are of one of $k$ types and in which edges appear and disappear independently of each other. We establish a functional law of large…
The dissertation is related to combinatorial geometry with a strong probabilistic flavor. The main results can be split into three parts. The results of the first part guarantee that each "unit distance graph" in the plane has an induced…
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…
In this paper we are concerned with contact processes with random vertex weights on oriented lattices. In our model, we assume that each vertex x of Z^d takes i. i. d. positive random value \rho(x). Vertex y infects vertex x at rate…
People change their physical contacts as a preventive response to infectious disease propagations. Yet, only a few mathematical models consider the coupled dynamics of the disease propagation and the contact adaptation process. This paper…