相关论文: Large deviations for infectious diseases models
Our paper investigates distributions of exposed and infectious time periods in an epidemic model and how applying a disease control strategy affects the model's accuracy. While ordinary differential equations are widely used for their…
In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of…
We study the susceptible-infective-recovered (SIR) epidemic on a random graph chosen uniformly subject to having given vertex degrees. In this model infective vertices infect each of their susceptible neighbours, and recover, at a constant…
We study epidemic models where the infectivity of each individual is a random function of the infection age (the elapsed time of infection). To describe the epidemic evolution dynamics, we use a stochastic process that tracks the number of…
Compartmental epidemic models, grounded in mass-action kinetics, often assume homogeneous mixing. Although this neglects network structure, recent results show that for Poisson random graphs, the classical SIR model, especially the…
Infectious disease dynamics operate across multiple biological scales, with within-host viral dynamics being a key driver of between-host transmission. However, while models that explicitly link these scales exist, none have been developed…
We extend our BDI (birth-death-immigration) process based stochastic model of an infectious disease to time-nonhomogeneous cases. First, we discuss the deterministic model, and derive the expected value of the infection process. Then as an…
The main results in this paper concern large deviations for families of non-Gaussian processes obtained as suitable perturbations of continuous centered multivariate Gaussian processes which satisfy a large deviation principle. We present…
Understanding the dynamics of the spread of diseases within populations is critical for effective public health interventions. We extend the classical SIR model by incorporating additional complexities such as the introduction of a cure and…
The issue of state estimation is considered for an SIR-SI epidemiological model describing a vector-borne disease such as dengue fever, subject to seasonal variations. Assuming continuous measurement of the incidence rate (that is the…
To model the evolution of diseases with extended latency periods and the presence of asymptomatic patients like COVID-19, we define a simple discrete time stochastic SIR-type epidemic model. We include both latent periods as well as the…
The configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. The component structure of such random graphs can be…
In this paper, we establish a large deviation principle for stochastic differential delay equations driven by both Brownian motions and Poisson random measures. The weak convergence method plays an important role.
Infection spread among individuals is modelled with a continuous time Markov chain, in which subject interactions depend on their distance in space. The well known SIR model and non local variants of the latter are then obtained as large…
Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate 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…
In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could…
Renewal processes are a popular approach used in modelling infectious disease outbreaks. In a renewal process, previous infections give rise to future infections. However, while this formulation seems sensible, its application to infectious…