Related papers: The Dynamics of a Vertically Transmitted Disease
We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the…
Multiple viruses are widely studied because of their negative effect on the health of host as well as on whole population. The dynamics of coinfection is important in this case. We formulated a SIR model that describes the coinfection of…
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…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…
SIRS epidemic models assume that individual immunity (from infection and vaccination) wanes in one big leap, from complete immunity to complete susceptibility. For many diseases immunity on the contrary wanes gradually, something that's…
This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between…
Social networks are an important infrastructure for information, viruses and innovations propagation. Since users behavior has influenced by other users activity, some groups of people would be made regard to similarity of users interests.…
We study some anisotropic heterogeneous nonlinear integral equations arising in epidemiology. We focus on the case where the heterogeneities are spatially periodic. In the first part of the paper, we show that the equations we consider…
The SIRS process is a continuous-time process for how infections spread on a graph. In this model, each vertex is in one of the following three states: susceptible (to the infection; S), infected (I), or recovered (R) and thus immune to the…
We consider a continuous-time Markov chain model of SIR disease dynamics with two levels of mixing. For this so-called stochastic households model, we provide two methods for inferring the model parameters---governing within-household…
A model based on a thermodynamic approach is proposed for predicting the dynamics of communicable epidemics in a city, when the epidemic is governed by controlling efforts of multiple scales so that an entropy is associated with the system.…
Age at infection is often an important factor in epidemic dynamics. In this paper a disease transmission model of SIS type with age dependent infection on a heterogeneous network is discussed. The model allows the infectious rate and the…
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…
This article is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Neumann boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous and…
We obtain conditions for eradication and permanence of infection for a nonautonomous SIQR model with time-dependent parameters, that are not assumed to be periodic. The incidence is given by functions of all compartments and the threshold…
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…
We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the…
We construct a set of new epidemiological thresholds to address the general problem of spreading and containment of a disease with influx of infected individuals when the classic $\mathcal R_0$ is no longer meaningful. We provide analytical…
We consider an epidemiological SIR model and a positive threshold $M$. Using a parametric expression for the solution curve of the SIR model and the Lambert W function, we establish necessary and sufficient conditions on the basic…
We consider an individual-based SIR stochastic epidemic model in continuous space. The evolution of the epidemic involves the rates of infection and cure of individuals. We assume that individuals move randomly on the two-dimensional torus…