Related papers: The Dynamics of a Vertically Transmitted Disease
Since 1927, until recently, models describing the spread of disease have mostly been of the SIR-compartmental type, based on the assumption that populations are homogeneous and well-mixed. The focus of these models have typically been on…
Consider a uniformly mixing population which grows as a super-critical linear birth and death process. At some time an infectious disease (of SIR or SEIR type) is introduced by one individual being infected from outside. It is shown that…
The dynamics of the spread of contagions such as viruses, infectious diseases or even rumors/opinions over contact networks (graphs) have effectively been captured by the well known \textit{Susceptible-Infected-Susceptible} ($SIS$) epidemic…
We formulate a multi-group and multi-vector epidemic model in which hosts' dynamics is captured by staged-progression $SEIR$ framework and the dynamics of vectors is captured by an $SI$ framework. The proposed model describes the evolution…
We propose a mathematical model to analyze the effects of anti-infection behavior on the equilibrium states of an infectious disease. The anti-infection behavior is incorporated into a classical epidemiological SIR model, by considering the…
We study the SIR epidemic model with infections carried by $k$ particles making independent random walks on a random regular graph. Here we assume $k\leq n^{\epsilon}$, where $n$ is the number of vertices in the random graph, and $\epsilon$…
In this paper, we are concerned with SIR epidemics in a random environment on complete graphs, where every edges are assigned with i.i.d. weights. Our main results give large and moderate deviation principles of sample paths of this model.
We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as…
We consider two approaches to study the spread of infectious diseases within a spatially structured population distributed in social clusters. According whether we consider only the population of infected individuals or both populations of…
In the study of infectious diseases on networks, researchers calculate epidemic thresholds to help forecast whether a disease will eventually infect a large fraction of a population. Because network structure typically changes in time,…
In this paper, we investigate the epidemic spreading for SIR model in weighted scale-free networks with nonlinear infectivity, where the transmission rate in our analytical model is weighted. Concretely, we introduce the infectivity…
A network epidemic model is studied. The underlying social network has two different types of group structures, households and workplaces, such that each individual belongs to exactly one household and one workplace. The random network is…
Understanding infectious disease spread remains a critical public health challenge, particularly given the interplay between household dynamics and community transmission patterns. Traditional epidemiological models often oversimplify these…
We study the effect of external infection sources on phase transitions in epidemic processes. In particular, we consider an epidemic spreading on a network via the SIS/SIR dynamics, which in addition is aided by external agents - sources…
This paper investigates a behavioral-feedback SIR model in which the infection rate adapts dynamically based on the fractions of susceptible and infected individuals. We introduce an invariant of motion and we characterize the peak of…
With the premise that social interactions are described by power-law distributions, we study a SIR stochastic dynamic on a static scale-free random network generated via configuration model. We verify our model with respect to deterministic…
We investigate the SIR epidemic on a dynamic inhomogeneous Erd\H{o}s-R\'enyi random graph, in which vertices are of one of $k$ types and in which edges appear and disappear independently of each other. We establish a functional law of large…
We study convergence properties of competing epidemic models of the Susceptible-Infected-Susceptible (SIS) type. The SIS epidemic model has seen widespread popularity in modelling the spreading dynamics of contagions such as viruses,…
We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…
This study focuses on analyzing a deterministic SIR model governing the dynamics of the hosts and vectors on an urban network. Our analysis scrutinizes the typical existence--stability of the equilibria as well as the sensitivity of the…