Related papers: Topological Degree Methods for Age-Structured Epid…
In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for…
A new age-structured diffusive model for the mathematical modelling of epidemics is suggested. The model can be considered as a generalization of two models suggested earlier for the same purposes. The Lie symmetry classification of the…
The main purpose of this paper is to study the local dynamics and bifurcations of a discrete-time SIR epidemiological model. The existence and stability of disease-free and endemic fixed points are investigated along with a fairly complete…
We present a methodology providing a one-directional link from within-host individual heterogeneity to population-level disease transmission dynamics. The methodology works in several steps. A within-host model is investigated numerically…
Mathematical modelling of the spread of epidemics has been an interesting challenge in the field of epidemiology. The SIR Model proposed by Kermack and McKendrick in 1927 is a prototypical model of epidemiology. However, it has its…
The main aim of the work is to present a general class of two time scales discrete-time epidemic models. In the proposed framework the disease dynamics is considered to act on a slower time scale than a second different process that could…
Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a…
Waning immunity and reinfection are critical features of many infectious diseases, but epidemiological models often fail to capture the intricate interaction between an individual's history of immunity and their current infection status;…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
This paper offers the first systematic presentation of the topological approach to the analysis of epidemic and pseudo-epidemic spatial processes. We introduce the basic concepts and proofs, at test the approach on a diverse collection of…
This paper focuses on and analyzes realistic SIR models that take stochasticity into account. The proposed systems are applicable to most incidence rates that are used in the literature including the bilinear incidence rate, the…
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…
In this article we have successfully obtained an exact solution of a particular case of SIR and SIS epidemic models given by Kermack and Mckendrick [1] for constant population, which are described by coupled nonlinear differential…
Traditional biomedical approaches treat diseases in isolation, but the importance of synergistic disease interactions is now recognized. As a first step we present and analyze a simple coinfection model for two diseases affecting…
A stochastic SIR epidemic model taking into account the heterogeneity of the spatial environment is constructed. The deterministic model is given by a partial differential equation and the stochastic one by a space-time jump Markov process.…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
Estimation of epidemiological and population parameters from molecular sequence data has become central to the understanding of infectious disease dynamics. Various models have been proposed to infer details of the dynamics that describe…
Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this…
In this paper we introduce an agent-based epidemiological model that generalizes the classical SIR model by Kermack and McKendrick. We further provide a multiscale approach to the derivation of a macroscopic counterpart via the mean-field…
Compartmental models, especially the Susceptible-Infected-Removed (SIR) model, have long been used to understand the behaviour of various diseases. Allowing parameters, such as the transmission rate, to be time-dependent functions makes it…