相关论文: Large deviations for infectious diseases models

In Part 1, we introduced a stochastic model of an infectious disease, based on the BDI (birth and death with immigration) process. We showed that random processes defined by this model can capture the essence of the stochastic, often…

Epidemics are often modelled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions,…

We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also…

We present a systematic review of some basic results on the derivation of classical epidemiological models from simple agent-based dynamics. The evolution of large populations is coupled with the dynamics of the contact distribution,…

We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her "age" of infection. We focus first on early outbreak stages when stochastic…

We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's…

Motivated by our intention to use SIR-type epidemiological models in the context of dynamic networks as provided by large-scale highly interacting inhomogeneous human crowds, we investigate in this framework possibilities to reduce the…

In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for…

Forecasting transmission of infectious diseases, especially for vector-borne diseases, poses unique challenges for researchers. Behaviors of and interactions between viruses, vectors, hosts, and the environment each play a part in…

We introduce a stochastic SIR-type partial differential equation model incorporating random diffusion, reinfection, vital dynamics, and a randomly varying transmission rate. For the associated random dynamical system, we prove the existence…

We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected. We prove that a…

We develop a framework for non-Markovian, well-mixed SIR and SIS models beyond mean field, utilizing the continuous-time random walk formalism. Using a gamma distribution for the infection and recovery inter-event times as a test case, we…

Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a…

The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…

We present a parsimonious stochastic model for valuation of options on the fraction of infected individuals during an epidemic. The underlying stochastic dynamical system is a stochastic differential version of the SIR model of mathematical…

Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…

In this work, we review the figures used to characterize an epidemic outbreak most. Particular attention is drawn to epidemic spreading at time-varying transition rates. A time-varying SIR-like model is used to describe the epidemic…

Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number $R_0$ determines their global dynamics. If $R_0\le 1$, then the frequency of…

The ubiquity of oscillations in epidemics presents a long standing challenge for the formulation of epidemic models. Whether they are external and seasonally driven, or arise from the intrinsic dynamics is an open problem. It is known that…

Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with…