Related papers: Global Stability of a Diffusive SEIR Epidemic Mode…
The SIR model with spatially inhomogeneous infection rate is studied with numerical simulations in one, two, and three dimensions, considering the case that the infection spreads inhomogeneously in densely populated regions or hot spots. We…
We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. We present a condition…
In this paper, we study an analytically tractable SIS model with a non-linear incidence rate for the number of infectious individuals described through a stochastic differential equation (SDE). We guarantee the existence of a positive…
The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to…
A retrovirus dynamic model is proposed. We pay attention to the case when viral pathogenicity is low and the infected cells are able to reproduce. Using Lyapunov function method we study stability properties of an inner equilibrium of the…
We study a diffusive SIS epidemic model with the mass-action transmission mechanism and show, under appropriate assumptions on the parameters, the existence of multiple endemic equilibria (EE). Our results answer some open questions on…
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,…
In this paper we propose a novel SEIR stochastic epidemic model. A distinguishing feature of this new model is that it allows us to consider a set up under general latency and infectious period distributions. To some extent, queuing systems…
In this paper, a global stability analysis is given for a rate-based congestion control system modeled by a nonlinear delayed differential equation. The model determines the dynamics of a single-source single-link network, with a…
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…
We will study a mathematical model of the human immunodeficiency virus (HIV) infection in the presence of combination therapy that includes within-host infectious dynamics. The deterministic model requires us to analyze asymptotic stability…
In this paper, we develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure…
In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a…
The ubiquity of oscillations in epidemics presents a long standing challenge for the formulation of epidemic models. Whether they are external and seasonally driven, or arise from the intrinsic dynamics is an open problem. It is known that…
In this paper, we study the global dynamics of epidemic network models with standard incidence or mass-action transmission mechanism, when the dispersal of either the susceptible or the infected people is controlled. The connectivity matrix…
This paper presents a novel time-space SIR (Susceptible-Infected-Recovered) model for simulating infectious disease dynamics in two interconnected regions. The model is formulated as a coupled reaction-diffusion system with boundary…
Public health services are constantly searching for new ways to reduce the spread of infectious diseases, such as public vaccination of asymptomatic individuals, quarantine (isolation) and treatment of symptomatic individuals. Epidemic…
The Susceptible-Exposed-Infectious-Recovered (SEIR) model is applied in several countries to ascertain the spread of the coronavirus disease 2019 (COVID-19). We consider discrete-time SEIR epidemic model in a closed system which does not…
We have derived the governing equations for an SIR model with delay terms in both the infectivity and recovery of the disease. The equations are derived by modelling the dynamics as a continuous time random walk, where individuals move…
We consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infection-induced mortality. We derive an infinite system of differential equations that provides an…