Related papers: Diffusion-Reaction Epidemic Model with a Free Boun…
Transmission dynamics of infectious diseases are often studied using compartmental mathematical models, which are commonly represented as systems of autonomous ordinary differential equations. A key step in the analysis of such models is to…
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…
Raw data on the cumulative number of deaths at a country level generally indicate a spatially variable distribution of the incidence of COVID-19 disease. An important issue is to determine whether this spatial pattern is a consequence of…
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 $\mathscr{R}_0$…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
We study the influence of heterogeneous mobility patterns in a population on the SIS epidemic model. In particular, we consider a patchy environment in which each patch comprises individuals belonging the different classes, e.g.,…
The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments…
In this paper, we analyze dynamic switching networks, wherein the networks switch arbitrarily among a set of topologies. For this class of dynamic networks, we derive an epidemic threshold, considering the SIS epidemic model. First, an…
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…
This paper continues to study the monostable cooperative system with nonlocal diffusion and free boundary, which has recently been discussed by [Du and Ni, 2020, arXiv:2010.01244]. We here aim at the four aspects: the first is to give more…
We study the spread of disease in an SIS model. The model considered is a time-varying, switched model, in which the parameters of the SIS model are subject to abrupt change. We show that the joint spectral radius can be used as a threshold…
The conceptual difference between equilibrium and non-equilibrium steady state (NESS) is well established in physics and chemistry. This distinction, however, is not widely appreciated in dynamical descriptions of biological populations in…
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. The authors have justified the well-posedness of this problem and have…
Medical statistics reveal a significant dependence of hospitalized dengue patient on the patient's age. To incorporate an age-dependence into a mathematical model, we extend the classical ODE system of disease dynamics to a PDE system. The…
A novel predictive modeling framework for the spread of infectious diseases using high dimensional partial differential equations is developed and implemented. A scalar function representing the infected population is defined on a…
Epidemics have shaped human history, often with devastating consequences, motivating the development of mathematical models to understand and control their dynamics. Among the many aspects of epidemic behavior, the conditions that lead to…
For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of…
We present a modified diffusive epidemic process that has a finite threshold on scale-free graphs. The diffusive epidemic process describes the epidemic spreading in a non-sedentary population, and it is a reaction-diffusion process. In the…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…
This paper is concerned with the spatio-temporal dynamics of an age-structured reaction-diffusion system of KPP-epidemic type (SIS), subject to Neumann boundary conditions and incorporating $L^1$ blow-up type death rate. We first establish…