Related papers: A kinetic model for epidemic spread
We study the spreading of an infection within an SIS epidemiological model on a network. Susceptible agents are given the opportunity of breaking their links with infected agents, and reconnecting those links with the rest of the…
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…
In contrast to the common assumption in epidemic models that the rate of infection between individuals is constant, in reality, an individual's viral load determines their infectiousness. We compare the average and individual reproductive…
The aim of this short note is twofold. We formulate the general Kermack-McKendrick epidemic model incorporating static heterogeneity and show how it simplifies to a scalar Renewal Equation (RE) when separable mixing is assumed. A key…
In the present paper the macroscopic limits of the kinetic model for inter-acting entities (individuals, organisms, cells) are studied. The kinetic model is one-dimensional and entities are characterized by their position and orientation…
A compartment epidemic model for infectious disease spreading is investigated, where movement of individuals is governed by spatial diffusion. The model includes infection age of the infected individuals and assumes a logistic growth of the…
We present an epidemiological compartment model, SAIR(S), that explicitly captures the dynamics of asymptomatic infected individuals in an epidemic spread process. We first present a group model and then discuss networked versions. We…
A kinetic model for granular mixtures is considered to study three different non-equilibrium situations. The model is based on the equivalence between a gas of elastic hard spheres subjected to a drag force proportional to the particle…
Viral kinetics have been extensively studied in the past through the use of spatially well-mixed ordinary differential equations describing the time evolution of the diseased state. However, emerging spatial structures such as localized…
We propose a kinetic model to describe the dynamical evolution of wealth and knowledge in national and global markets, starting from a microscopic description of individual interactions. The model is built upon interaction rules that…
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…
The size and shape of the region affected by an outbreak is relevant to understand the dynamics of a disease and help to organize future actions to mitigate similar events. A simple extension of the SIR model is considered, where agents…
One of the major issues in the theoretical modeling of epidemic spreading is the development of methods to control the transmission of an infectious agent. Human behavior plays a fundamental role in the spreading dynamics and can be used to…
We study the long-time behavior of solutions of the SIRS model, a reaction-diffusion system that appears in epidemiology to describe the spread of epidemics. We allow the system to be heterogeneous periodic. Under some hypotheses on the…
We study a simple realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population,…
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…
Networked SIR models have become essential workhorses in the modeling of epidemics, their inception, propagation and control. Here, and building on this venerable tradition, we report on the emergence of a remarkable self-organization of…
We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic…
In general, the rates of infection and removal (whether through recovery or death) are nonlinear functions of the number of infected and susceptible individuals. One of the simplest models for the spread of infectious diseases is the SIR…
Characterizing the spatial extent of epidemics at the outbreak stage is key to controlling the evolution of the disease. At the outbreak, the number of infected individuals is typically small, so that fluctuations around their average are…