Related papers: A nonautonomous epidemic model with general incide…
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…
The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…
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…
The classic SIR model of epidemic dynamics is solved completely by quadratures, including a time integral transform expanded in a series of incomplete gamma functions. The model is also generalized to arbitrary time-dependent infection…
A stochastic epidemic model is defined in which each individual belongs to a household, a secondary grouping (typically school or workplace) and also the community as a whole. Moreover, infectious contacts take place in these three settings…
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…
We study a multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population…
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…
We consider a susceptible, infected, removed (SIR) system where the transmission rate may be temporarily reduced for a fixed amount of time. We show that in order to minimize the total number of fatalities, the transmission rate should be…
In this manuscript, we develop a mobility-based Susceptible-Infectious-Recovered (SIR) model to elucidate the dynamics of pandemic propagation. While traditional SIR models within the field of epidemiology aptly characterize transitions…
The COVID-19 pandemic has emphasized the need for a robust understanding of epidemic models. Current models of epidemics are classified as either mechanistic or non-mechanistic: mechanistic models make explicit assumptions on the dynamics…
In this paper, we consider a discrete-time stochastic SIR model, where the transmission rate and the true number of infectious individuals are random and unobservable. An advantage of this model is that it permits us to account for random…
Dynamic properties of spreading infection through a heterogeneous population are studied numerically and analytically using a dynamic variant of Watts and Strogatz Small World Network-based stochastic Susceptible-Exposed-Infectious-Removed…
We consider a nonautonomous eco-epidemiological model with general functions for predation on infected and uninfected preys as well as general functions associated to the vital dynamics of the susceptible prey and predator populations. We…
This paper is concerned with two frequency-dependent SIS epidemic reaction-diffusion models in heterogeneous environment, with a cross-diffusion term modeling the effect that susceptible individuals tend to move away from higher…
In this paper, we further investigate the global dynamics of a stochastic differential equation SIS (Susceptible-Infected-Susceptible) epidemic model recently proposed in [A. Gray et al., SIAM. J. Appl. Math., 71 (2011), 876-902]. We…
The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…
This paper studies qualitative properties of solutions of nonlocal infectious SIR epidemic models (1.3)-(1.5), with the homogeneous Neumann boundary conditions, Dirichlet boundary conditions and free boundary, respectively. We first use the…
We study the minimum eradication time problem for controlled Susceptible-Infected-Recovered (SIR) epidemic models that incorporate vaccination control and time-varying infected and recovery rates. Unlike the SIR model with constant rates,…
We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from…