相关论文: Size of Outbreaks Near the Epidemic Threshold
We study the Susceptible-Infected-Recovered model of epidemics in the vicinity of the threshold infectivity. We derive the distribution of total outbreak size in the limit of large population size $N$. This is accomplished by mapping the…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
Power-law scalings are ubiquitous to physical phenomena undergoing a continuous phase transition. The classic Susceptible-Infectious-Recovered (SIR) model of epidemics is one such example where the scaling behavior near a critical point has…
The spread of an epidemic process is considered in the context of a spatial SIR stochastic model that includes a parameter $0\le p\le 1$ that assigns weights $p$ and $1- p$ to global and local infective contacts respectively. The model was…
We consider an infectious disease spreading along the edges of a network which may have significant clustering. The individuals in the population have heterogeneous infectiousness and/or susceptibility. We define the out-transmissibility of…
Multiple-type branching processes that model the spread of infectious diseases are investigated. In these stochastic processes, the disease goes through multiple stages before it eventually disappears. We mostly focus on the critical…
We model an epidemic where the per-person infectiousness in a network of geographic localities changes with the total number of active cases. This would happen as people adopt more stringent non-pharmaceutical precautions when the…
We study the Susceptible-Infected-Susceptible model of the spread of an endemic infection. We calculate an exact expression for the mean number of transmissions for all values of the population and the infectivity. We derive the large-N…
Incorporating dynamic contact networks and delayed awareness into a contagion model with memory, we study the spreading patterns of infectious diseases in connected populations. It is found that the spread of an infectious disease is not…
Characterizing the spatial extent of epidemics at the outbreak stage is key to controlling the evolution of the disease. At the outbreak, the number of infected individuals is typically small, so that fluctuations around their average are…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…
Understanding the timing of the peak of a disease outbreak forms an important part of epidemic forecasting. In many cases, such information is essential for planning increased hospital bed demand and for designing of public health…
Networks of person-person contacts form the substrate along which infectious diseases spread. Most network-based studies of the spread focus on the impact of variations in degree (the number of contacts an individual has). However, other…
We study epidemic spreading processes in large networks, when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\`a-vis the underlying network…
We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws…
In this work, we use a new approach to study the spread of an infectious disease. Indeed, we study a SIR epidemic model with variable infectivity, where the individuals are distributed over a compact subset $D$ of $\R^d$. We define…
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…
Epidemiological processes are studied within a recently proposed hierarchical network model using the susceptible-infected-refractory dynamics of an epidemic. Within the network model, a population may be characterized by $H$ independent…
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent $p-$coin tosses. Spatial variants of these models are proposed, in which finite…