Related papers: Epidemics: towards understanding undulation and de…
\noindent We formulate an age-structured three-staged nonlinear partial differential equation model that features {\it nonlinear} recidivism to the infected ({\it infectious}) class from the {\it temporarily} recovered class. Equilibria are…
In this paper, we give a complete analysis of an SIS epidemiological model in a population of varying size with two dissimilar groups of infective individuals. It is mainly based on the discussion of the existence and stability of…
Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior.…
In this article a space-dependent epidemic model equipped with a constant latency period is examined. We construct a delay partial integro-differential equation and show that its solution possesses some biologically reasonable features. We…
Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the…
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 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…
Motivated by analogies between the spreading of human-to-human infections and of chemical processes, we develop a comprehensive model that accounts both for infection and for transport. In this analogy, the three different populations of…
The emergence or adaptation of pathogens may lead to epidemics, highlighting the need for a thorough understanding of pathogen evolution. The tradeoff hypothesis suggests that virulence evolves to reach an optimal transmission intensity…
The infection dynamics of a population under stationary isolation conditions is modeled. It is underlined that the stationary character of the isolation measures can be expected to imply that an effective SIR model with constant parameters…
The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are…
Recent work by Erik Volz [arXiv:0705.2092] has shown how to calculate the growth and eventual decay of an SIR epidemic on a static random network, assuming infection and recovery each happen at constant rates. This calculation allows us to…
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…
A class of multiple-timescale asymptotic solutions to the equations of the susceptible-infected-recovered (SIR) model is presented for the case of high basic reproduction number, with the inverse of the latter employed as the expansion…
We study the qualitative properties of a spatial diffusive heterogeneous SIR model, that appears in mathematical epidemiology to describe the spread of an infectious disease in a population. The model we consider consists in a system of…
We investigate final outcome properties of an SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a population of large sub-communities in which there is stronger disease transmission within the communities than…
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…
This paper studies a distributed continuous-time bi-virus model in which two competing viruses spread over a network consisting of multiple groups of individuals. Limiting behaviors of the network are characterized by analyzing the…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…
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. Broken links are either permanently removed or reconnected…