Related papers: A spatially varying differential equation for mult…
In this work, the spread of a contagious disease on a society where the individuals may take precautions is modeled. The primary assumption is that the infected individuals transmit the infection to the susceptible members of the community…
We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three…
Partial differential equation (PDE) models for infectious disease have received renewed interest in recent years. Most models of this type extend classical compartmental formulations with additional terms accounting for spatial dynamics,…
The Susceptible-Infected-Recovered (SIR) epidemic model is extensively used for the study of the spread of infectious diseases. Even that the exact solution of the model can be obtained in an exact parametric form, in order to perform the…
This paper studies novel epidemic spreading problems influenced by opinion evolution in social networks, where the opinions reflect the public health concerns. A coupled bilayer network is proposed, where the epidemics spread over several…
Contact patterns in populations fundamentally influence the spread of infectious diseases. Current mathematical methods for epidemiological forecasting on networks largely assume that contacts between individuals are fixed, at least for the…
We study dynamics of a variant of the SIR the model, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. The degree of heterogeneity…
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 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…
Using a probability of novel encounter derived from a physical model, we augment the SIR compartmental model for disease spread. Scenarios with the same initial trajectories and identical $R_0$ values can diverge greatly depending on the…
Partial differential equation (PDE) models for infectious diseases, while less common than their ordinary differential equation (ODE) counterparts, have found successful applications for many years. Such models are typically of…
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent $p-$coin tosses. Spatial variants of these models are proposed, in which finite…
In this short note we model the region-wise trends of the evolution to COVID-19 infections using a stochastic SIR model. The SIR dynamics are expressed using \textit{It\^o-stochastic differential equations}. We first derive the parameters…
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…
This paper is concerned with SIR (susceptible $\to$ infected $\to$ removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an…
We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is comprised of a system of ordinary differential equations…
In this work, we discuss the SIR epidemiological model and different variations of it applied to the propagation of the COVID-19 pandemia; we employ the data of the state of Guanajuato and of Mexico. We present some considerations that can…
The global pandemic due to the outbreak of COVID-19 ravages the whole world for more than two years in which all the countries are suffering a lot since December 2019. In order to control this ongoing waves of epidemiological infections,…
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…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…