Related papers: A nonlinear cross-diffusion epidemic with time-dep…
The SIR model is a classical model characterizing the spreading of infectious diseases. This model describes the time-dependent quantity changes among Susceptible, Infectious, and Recovered groups. By introducing space-depend effects such…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
We propose a nonstandard finite difference scheme for the Susceptible-Infected-Removed (SIR) continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution.…
This article is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and…
We study the spread of discrete-time epidemics over arbitrary networks for well-known propagation models, namely SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered), SIRS (susceptible-infected-recovered-susceptible)…
Although we have made progress in understanding disease spread in complex systems with non-Poissonian activity patterns, current models still fail to capture the full range of recovery time distributions. In this paper, we propose an…
This paper is concerned with the well-posedness of a diffusion-reaction system for a Susceptible-Exposed-Infected-Recovered (SEIR) mathematical model. This model is written in terms of four nonlinear partial differential equations with…
Motivated by the ongoing pandemic COVID-19, we propose a closed-loop framework that combines inference from testing data, learning the parameters of the dynamics and optimal resource allocation for controlling the spread of the…
Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…
To better describe the spread of a disease, we extend a discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We assume the dependence on time of the number of daily encounters and include a parameter to represent a…
We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…
In this article, we construct a numerical method for a stochastic version of the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a suitable stochastic differential equation (SDE), by using the semi-discrete method to a…
The coronavirus pandemic has rapidly evolved into an unprecedented crisis. The susceptible-infectious-removed (SIR) model and its variants have been used for modeling the pandemic. However, time-independent parameters in the classical…
The COVID-19 pandemic highlighted the need to improve the modeling, estimation, and prediction of how infectious diseases spread. SEIR-like models have been particularly successful in providing accurate short-term predictions. This study…
Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the…
Diffusion of information in networks is at the core of many problems in AI. Common examples include the spread of ideas and rumors as well as marketing campaigns. Typically, information diffuses at a non-linear rate, for example, if markets…
We introduce a kinetic model that couples the movement of a population of individuals with the dynamics of a pathogen in the same population. We consider that transmission occurs when a susceptible and an infectious individual are…
The non-population conserving SIR (SIR-NC) model to describe the spread of infections in a community is proposed and studied. Unlike the standard SIR model, SIR-NC does not assume population conservation. Although similar in form to the…