Related papers: On a model for epidemic spread with interpopulatio…
In this manuscript, an attempt has been made to understand the effects of prey-taxis on the existence of global-in-time solutions and dynamics in an eco-epidemiological model, particularly under the influence of slow dispersal characterized…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
We study epidemic arrival times in meta-population disease models through the lens of front propagation into unstable states. We demonstrate that several features of invasion fronts in the PDE context are also relevant to the network case.…
We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is based on a kinetic description at discrete velocities of the…
In this work we propose a novel space-dependent multiscale model for the spread of infectious diseases in a two-dimensional spatial context on realistic geographical scenarios. The model couples a system of kinetic transport equations…
We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
We consider the qualitative behavior of a mathematical model for transmission dynamics with two nonlinear stages of contagion. The proposed model is inspired by phenomena occurring in epidemiology (spread of infectious diseases) or social…
This paper studies an epidemic model with nonlocal dispersals. We focus on the influences of initial data and nonlocal dispersals on its spatial propagation. Here the initial data stand for the spatial concentrations of infectious agent and…
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,…
We present a simple model for the spread of an infection that incorporates spatial variability in population density. Starting from first principle considerations, we explore how a novel PDE with state-dependent diffusion can be obtained.…
Motile organisms can form stable agglomerates such as cities or colonies. In the outbreak of a highly contagious disease, the control of large-scale epidemic spread depends on factors like the number and size of agglomerates, travel rate…
Despite the advanced stage of epidemic modeling, there is a major demand for methods to incorporate behavioral responses to the spread of a disease such as social distancing and adoption of prevention methods. Mobility plays an important…
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…
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…
This paper establishes existence, uniqueness, and an L^1-comparison principle for weak solutions of a PDE system modeling phase transition reaction-diffusion in congested crowd motion. We consider a general reaction term and mixed…
We consider a model for an epidemic in a population that occupies geographically distinct locations. The disease is spread within subpopulations by contacts between infective and susceptible individuals, and is spread between subpopulations…
In the Staged Progression (SP) epidemic models, infected individuals are classified into a suitable number of states. The goal of these models is to describe as closely as possible the effect of differences in infectiousness exhibited by…
We propose and study a new model to describe biological invasions constrained on infinite homogeneous one dimensional metric graphs. Our model consists of an infinite PDE-ODE system where, at each vertex of the one-dimensional lattice…
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…