Related papers: Social contact processes and the partner model
We study an infection-age structured epidemic model in which both the infectivity and the rate of loss of immunity depend on the time-since-infection. The model can be equivalently viewed as a nonlinear renewal equation for the incidence of…
We argue that the time from the onset of infectiousness to infectious contact, which we call the contact interval, is a better basis for inference in epidemic data than the generation or serial interval. Since contact intervals can be…
We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a…
We study the spreading of an infection within an SIS epidemiological model on a network. Susceptible agents are given the opportunity of breaking their links with infected agents. Broken links are either permanently removed or reconnected…
We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction number $\mathcal{R}_0$ of the pathogen can be defined in that…
Global strategies to contain a pandemic, such as social distancing and protective measures, are designed to reduce the overall transmission rate between individuals. Despite such measures, essential institutions, including hospitals,…
We formulate a general age-of-infection epidemic model with two pathways: the symptomatic infections and the asymptomatic infections. We then calculate the basic reproduction number $\mathcal{R}_0$ and establish the final size relation. It…
We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all…
Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using…
On a geometric model for complex networks (introduced by Krioukov et al.) we investigate the bootstrap percolation process. This model consists of random geometric graphs on the hyperbolic plane having $N$ vertices, a dependent version of…
We study the SIR epidemic model with infections carried by $k$ particles making independent random walks on a random regular graph. Here we assume $k\leq n^{\epsilon}$, where $n$ is the number of vertices in the random graph, and $\epsilon$…
This paper is a further study of Reference \cite{Xue2015}. We are concerned with the contact process with random vertex weights on the oriented lattice. Our main result gives the asymptotic behavior of the survival probability of the…
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…
An important issue in theoretical epidemiology is the epidemic threshold phenomenon, which specify the conditions for an epidemic to grow or die out. In standard (mean-field-like) compartmental models the concept of the basic reproductive…
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 the standard SIR model, infected vertices infect their neighbors at rate $\lambda$ independently across each edge. They also recover at rate $\gamma$. In this work we consider the SIR-$\omega$ model where the graph structure itself…
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…
This article is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and…
We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic…
The basic reproduction number, $R_0$, is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating $R_0$ from incidence data early in the epidemic can lead to an over-estimation of this quantity. In…