Related papers: The deterministic Kermack-McKendrick model bounds …

We consider a general class of epidemic models obtained by applying a random time change to a collection of Poisson processes and we show the large deviation principle for such models. We generalize to a more general situation the approach…

This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate $\omega$ (and reconnect to non-infectious individuals with probability…

In this work we look at several mathematical models that have been constructed during the present pandemic to address dfferent issues of importance to public health policies about epidemic scenarios and thier causes. We start by briefly…

We consider a stochastic susceptible-infected-recovered (SIR) model with contact tracing on random trees and on the configuration model. On a rooted tree, where initially all individuals are susceptible apart from the root which is…

We present an algebraic solution for the Susceptible-Infective-Removed (SIR) model originally presented by Kermack-McKendrick in 1927. Starting from the differential equation for the removed subjects presented by them in the original paper,…

We study the deterministic Susceptible-Infected-Susceptible (SIS) epidemic model on weighted graphs. In their numerical study [10] van Mieghem et al. have shown that it is possible to learn an estimated network from a finite time sample of…

We study the critical effect of an intermittent social distancing strategy on the propagation of epidemics in adaptive complex networks. We characterize the effect of our strategy in the framework of the susceptible-infected-recovered…

Susceptible-Exposed-Infectious-Recovered (SEIR) models with inter-individual variation in susceptibility or exposure to infection were proposed early in the COVID-19 pandemic as a potential element of the mathematical/statistical toolset…

This paper utilizes a stochastic Susceptible-Infected-recovered (SIR) model with a non-linear incidence rate to perform a detailed mathematical study of optimal lock-down intensity and vaccination rate under the COVID-19 pandemic…

Exact solution of the Susceptible-Infectious-Recovered (SIR) epidemic model is derived, and various properties of solution are obtained directly from the exact solution. It is shown that there exists an exact solution of an initial value…

In this paper, we are concerned with the stochastic SIS (susceptible-infected-susceptible) and SIR (susceptible-infected-recovered) models on high-dimensional lattices with random edge weights, where a susceptible vertex is infected by an…

Stochastic epidemic models provide an interpretable probabilistic description of the spread of a disease through a population. Yet, fitting these models to partially observed data is a notoriously difficult task due to intractability of the…

This paper considers the classical SIR epidemic model driven by a multidimensional L\'evy jump process. We consecrate to develop a mathematical method to obtain the asymptotic properties of the perturbed model. Our method differs from…

We extend the classical Susceptible-Infected-Recovered (SIR) model to a network-based framework where the degree distribution of nodes follows a Poisson distribution. This extension incorporates an additional parameter representing the mean…

We study a well mixed SIR epidemic model with heterogeneous susceptibility and infectivity, allowing for an arbitrary joint distribution of these traits. Using an exact final size formulation and a branching process approximation for early…

This paper provides an additional probabilistic interpretation of the limiting functions for the SIR epidemic on the configuration model derived in the paper by Janson, Luczak and Windridge (2014).

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…

Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that…

Estimation of epidemiological and population parameters from molecular sequence data has become central to the understanding of infectious disease dynamics. Various models have been proposed to infer details of the dynamics that describe…

We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…