相关论文: An infection process near criticality: Influence o…
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…
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…
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…
We consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations…
In the study of epidemic dynamics a fundamental question is whether a pathogen initially affecting only one individual will give rise to a limited outbreak or to a widespread pandemic. The answer to this question crucially depends not only…
We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching…
The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but do not incorporate population-level heterogeneity in infection susceptibility.…
We have investigated the effect of the initial condition on the spreading exponents of the one-dimensional pair contact process (PCP) and threshold transfer process (TTP).The non-order field was found to exhibit critical fluctuations,…
Quarantine measures are one of the first lines of defense against the spread of infectious diseases. However, maintaining these measures over extended periods can be challenging due to a phenomenon known as quarantine fatigue. In this…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
When an infection spreads in a community, an individual's probability of becoming infected depends on both her susceptibility and exposure to the contagion through contact with others. While one often has knowledge regarding an individual's…
We consider the SIR model and study the first time the number of infected individuals begins to decrease and the first time this population is below a given threshold. We interpret these times as functions of the initial susceptible and…
Background: Recently developed techniques to study the spread of infectious diseases through networks make assumptions that the initial proportion infected is infinitesimal and the population behavior is static throughout the epidemic. The…
The spread of infectious diseases near the epidemic threshold is investigated. Scaling laws for the size and the duration of outbreaks originating from a single infected individual in a large susceptible population are obtained. The maximal…
In the first part of this paper, we review old and new results about the influence of host population heterogeneity on (various characteristics of) epidemic outbreaks. In the second part we highlight a modelling issue that so far has…
Human mobility and activity patterns mediate contagion on many levels, including the spatial spread of infectious diseases, diffusion of rumors, and emergence of consensus. These patterns however are often dominated by specific locations…
The diffusive epidemic process is a paradigmatic example of an absorbing state phase transition in which healthy and infected individuals spread with different diffusion constants. Using stochastic activity spreading simulations in…
We consider branching process evolving in i.i.d. random environment. It is assumed that the process is intermediately subcritical. We investigate the initial stage of the evolution of the process given its survival for a long time.
Containment measures implemented by some countries to suppress the spread of COVID-19 have resulted in a slowdown of the epidemic characterized by time series of daily infections plateauing over extended periods of time. We prove that such…
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…