相关论文: Multiple Equilibria for an SIRS Epidemiological Sy…
We study dynamics of a variant of the SIR the model, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. The degree of heterogeneity…
TThis paper presents the dynamics of mosquitoes and humans, with general nonlinear incidence rate and multiple distributed delays for the disease. The model is a SEIRS system of delay differential equations. The normalized dimensionless…
We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of…
Treatment rate has always been one of the most important factors affecting the spread of infectious diseases. In this paper, we study a treatment function SIR model with treatment rate related to the maximum treatment capacity, whose…
We define and study an open stochastic SIR (Susceptible -- Infected -- Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same…
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected…
In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic SIR epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR…
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…
An ultrametric model of epidemic spread of infections based on the classical SIR model is proposed. Ultrametrics on a set of individuals based on theire hierarchical clustering relativly to the average time of infectious contact is…
The focus of this article is on the dynamics of a new susceptible-infected model which consists of a susceptible group ($S$) and two different infectious groups ($I_1$ and $I_2$). Once infected, an individual becomes a member of one of…
Starting from common assumptions, we build a rate equation model for multi-strain disease dynamics in terms of immune repertoire classes. We then move to a strain-level description where a low-order closure reminiscent of a pair…
An SIR epidemic model with free boundary is investigated. This model describes the transmission of diseases. The behavior of positive solutions to a reaction-diffusion system in a radially symmetric domain is investigated. The existence and…
Complex networks with pairwise connections have been vastly used for the modeling of interactions within systems. Although these type of models are capable to capture rich structures and different phases within a great variety of…
An epidemic Susceptible-Vaccinated-Infected-Removed-Susceptible (SVIRS) model is presented on a weighted-undirected network with graph Laplacian diffusion. Disease-free equilibrium always exists while the existence and uniqueness of endemic…
We introduce an extension to Kermack and McKendrick's classic susceptible-infected-recovered (SIR) model in epidemiology, whose underlying mechanism of infection consists of individuals attending randomly generated social gatherings. This…
It has been known that epidemic outbreaks in the SIR model on networks are described by phase transitions. Despite the similarity with percolation transitions, whether an epidemic outbreak occurs or not cannot be predicted with probability…
This is work in progress. We make it accessible hoping that people might find the idea useful. We propose a discrete, recursive 5-compartment model for the spread of epidemics, which we call {\em SEPIR-model}. Under mild assumptions which…
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological…
We formulate a generalized susceptible exposed infectious recovered (SEIR) model on a graph, describing the population dynamics of an open crowded place with an arbitrary topology. As a sample calculation, we discuss three simple cases,…
Most epidemic models are spatially aggregate and the index which is most used for planning and policy numbers, the r number, typically refers to a single system of interest. Even if r numbers are calculated for each of adjacent areas,…