Related papers: Propagation properties in a multi-species SIR reac…
In this work, we study the epidemic SIR model on a system which takes into consideration face-to-face interaction networks. This approach has been used as prototype to describe people interactions in different kinds of social organizations…
Small and large scale pandemics are a natural phenomenon repeatably appearing throughout history, causing ecological and biological shifts in ecosystems and a wide range of their habitats. These pandemics usually start with a single strain…
This paper deals with a new epidemiological model of SIRS with stochastic perturbations. The primary objective is to establish the existence of a unique non-negative nonlocal solution. Using the basic reproduction number $\mathscr{R}_0$…
We have designed a computational model of a virus spread near the outbreak threshold. Using computer simulation we studied the Susceptible - Infected - Recovered (SIR) process where in consequence of a force of habit that is manifested by…
The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…
The SIR model is used extensively in the field of epidemiology, in particular, for the analysis of communal diseases. One problem with SIR and other existing models is that they are tailored to random or Erdos type networks since they do…
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…
We present a mathematical study for the development of multiple sclerosis based on a reaction-diffusion system. The model describes interactions among different populations of human cells, motion of immune cells stimulated by cytokines,…
The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. Here we consider a model of diffusion where the individuals' behavior is the result of a strategic choice. We study a simple coordination…
The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the…
The paper describes and compares three approaches to modeling an epidemic spread. The first approach is a well-known system of SIR ordinary differential equations. The second is a mean-field model, in which an isolation strategy for each…
An understanding of the disease spreading phenomenon based on a mathematical model is extremely needed for the implication of the correct policy measures to contain the disease propagation. Here, we report a new model namely the Ising-SIR…
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…
We introduce an extension to Kermack and McKendrick's classic susceptible-infected-recovered (SIR) model in epidemiology, whose underlying mechanism of infection consists of individuals attending randomly generated social gatherings. This…
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological…
The spread of infectious disease and the evolution of antigenically distinct strains are often modeled separately, despite strong feedbacks mediated by host immune memory and heterogeneous contacts. To tackle this challenging problem, we…
We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic…
The goal of this work is to understand and quantify how a line with nonlocal diffusion given by an integral enhances a reaction-diffusion process occurring in the surrounding plane. This is part of a long term programme where we aim at…
We consider the emergent behavior of viral spread when agents in a large population interact with each other over a contact network. When the number of agents is large and the contact network is a complete graph, it is well known that the…
The ability to actually implement epidemic models is a crucial stake for public institutions, as they may be overtaken by the increasing complexity of current models and sometimes tend to revert to less elaborate models such as the SIR. In…