Related papers: Universal features of epidemic and vaccine models
In this paper, we focus on the influence of heterogeneity and stochasticity of the population on the dynamical structure of a basic susceptible-infected-susceptible (SIS) model. First we prove that, upon a suitable mathematical…
In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…
In this study, a new and natural way of constructing a stochastic Susceptible-Infected-Susceptible (SIS) model is proposed. This approach is natural in the sense that the disease transmission rate, $\beta$, is substituted with a generic,…
Some recent works reveal that there are models of differential equations for the mean and variance of infected individuals that reproduce the SIS epidemic model at some point. This stochastic SIS epidemic model can be interpreted as a…
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…
This work consists of an epidemic model with vaccination coupled with an opinion dynamics. Our objective was to study how disease risk perception can influence opinions about vaccination and therefore the spreading of the disease.…
This paper considers a mathematical model based on the transmission dynamics of hepatitis C virus (HCV) infection. In addition to the usual compartments for susceptible, exposed, and infected individuals, this model includes compartments…
One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the…
In this paper, a susceptible-infected-susceptible (SIS) model with identical infectivity, where each node is assigned with the same capability of active contacts, $A$, at each time step, is presented. We found that on scale-free networks,…
The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile…
This paper considers a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and varying total population. The interaction of the susceptible and infected people is describe by the…
Here, we consider an SIS epidemic model where the individuals are distributed on several distinct patches. We construct a stochastic model and then prove that it converges to a deterministic model as the total population size tends to…
This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic model properties (relying on a large community) are presented. The purpose of modelling is illustrated by…
Epidemics have shaped human history, often with devastating consequences, motivating the development of mathematical models to understand and control their dynamics. Among the many aspects of epidemic behavior, the conditions that lead to…
There are few adapted SIR models in the literature that combine vaccination and logistic growth. In this article, we study bifurcations of a SIR model where the class of Susceptible individuals grows logistically and has been subject to…
The spreading of infectious diseases with and without immunization of individuals can be modeled by stochastic processes that exhibit a transition between an active phase of epidemic spreading and an absorbing phase, where the disease dies…
This paper focuses on the analysis of a stochastic SAIRS-type epidemic model that explicitly incorporates the roles of asymptomatic and symptomatic infectious individuals in disease transmission dynamics. Asymptomatic carriers, often…
We propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density function, have duly been computed. Our models, which generalises a…
In this work we consider a model of epidemic spreading coupled with an opinion dynamics in a fully-connected population. Regarding the opinion dynamics, the individuals may be in two distinct states, namely in favor or against a vaccination…
We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals…