Related papers: Bayesian Tracking of Emerging Epidemics Using Ense…
Epidemic models play a key role in understanding and responding to the emerging COVID-19 pandemic. Widely used compartmental models are static and are of limited use to evaluate intervention strategies with the emerging pandemic. Applying…
The transmission dynamics of an epidemic are rarely homogeneous. Super-spreading events and super-spreading individuals are two types of heterogeneous transmissibility. Inference of super-spreading is commonly carried out on secondary case…
The SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable…
In this article, we develop a data assimilation procedure to predict the evolution of epidemics with data uncertainty, with application to the Covid-19 pandemic. We construct a vademecum of solutions by solving the SIR epidemic model for a…
In this paper, we develop a method to estimate the infection-rate of a disease, over a region, as a field that varies in space and time. To do so, we use time-series of case-counts of symptomatic patients as observed in the areal units that…
The widely used susceptible-infected-recovered (S-I-R) epidemic model assumes a uniform, well-mixed population, and incorporation of spatial heterogeneities remains a major challenge. Understanding failures of the mixing assumption is…
Recently the A/H1N1-2009 virus pandemic appeared in Mexico and in other nations. We present a study of this pandemic in the Mexican case using the SIR model to describe epidemics. This model is one of the simplest models but it has been a…
We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the…
The effect of spatial correlations on the spread of infectious diseases was investigated using a stochastic SIR (Susceptible-Infective-Recovered) model on complex networks. It was found that in addition to the reduction of the effective…
This paper investigates the spread of infectious diseases within a networked community by integrating epidemic transmission and public opinion dynamics. We propose a novel discrete-time networked SIS (Susceptible-Infectious-Susceptible)…
We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the…
We study several bayesian inference problems for irreversible stochastic epidemic models on networks from a statistical physics viewpoint. We derive equations which allow to accurately compute the posterior distribution of the time…
We consider the problem of identifying the source of an epidemic, spreading through a network, from a complete observation of the infected nodes in a snapshot of the network. Previous work on the problem has often employed geometric,…
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…
The availability of geocoded health data and the inherent temporal structure of communicable diseases have led to an increased interest in statistical models and software for spatio-temporal data with epidemic features. The open source R…
This paper introduces a novel hybrid model combining Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) to simulate infectious disease dynamics across geographic regions. By leveraging the spatial detail of…
Predicting the evolution of diseases is challenging, especially when the data availability is scarce and incomplete. The most popular tools for modelling and predicting infectious disease epidemics are compartmental models. They stratify…
Mutations sometimes increase contagiousness for evolving pathogens. During an epidemic, scientists use viral genome data to infer a shared evolutionary history and connect this history to geographic spread. We propose a model that directly…
Understanding age-group dynamics of infectious diseases is a fundamental issue for both scientific study and policymaking. Age-structure epidemic models were developed in order to study and improve our understanding of these dynamics. By…
Mathematical models of epidemic dynamics offer significant insight into predicting and controlling infectious diseases. The dynamics of a disease model generally follow a susceptible, infected, and recovered (SIR) model, with some standard…