相关论文: Vaccinating according to the maximal endemic equil…
In this article, we introduce an infinite-dimensional deterministic SIS model which takes into account the heterogeneity of the infections and the social network among a large population. We study the long-time behavior of the dynamic. We…
We formalize and study the problem of optimal allocation strategies for a (perfect) vaccine in the infinite-dimensional SIS model. The question may be viewed as a bi-objective minimization problem, where one tries to minimize simultaneously…
We examine here the effects of recurrent vaccination and waning immunity on the establishment of an endemic equilibrium in a population. An individual-based model that incorporates memory effects for transmission rate during infection and…
We consider an infinite-dimension SIS model introduced by Delmas, Dronnier and Zitt, with a more general incidence rate, and study its equilibria. Unsurprisingly, there exists at least one endemic equilibrium if and only if the basic…
This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral…
In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of…
We present a series of SIR-network models, extended with a game-theoretic treatment of imitation dynamics which result from regular population mobility across residential and work areas and the ensuing interactions. Each considered…
We study a multi-group SAIRS-type epidemic model with vaccination. The role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission pattern of the disease among the groups in which the population…
Network-based epidemic models have been extensively employed to understand the spread of infectious diseases, but have generally overlooked the fact that most realistic networks are dynamical rather than static. In this paper, we study a…
In this paper we consider epidemic models of directly transmissible SIR (susceptible $\to$ infective $\to$ recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting…
We study in a general mathematical framework the optimal allocation of vaccine in an heterogeneous population. We cast the problem of optimal vaccination as a bi-objective minimization problem min(C($\eta$),L($\eta$)), where C and L stand…
We propose and solve an optimal vaccination problem within a deterministic compartmental model of SIRS type: the immunized population can become susceptible again, e.g.\ because of a not complete immunization power of the vaccine. A social…
We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. We present a condition…
We analyse an extended SIRS epidemic model in which immunity at the individual level wanes gradually at exponential rate, but where the waning rate may differ between individuals, for instance as an effect of differences in immune systems.…
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…
This present results lay the foundations for the study of the optimal allocation of vaccine in the simple epidemiological SIS model where one consider a very general heterogeneous population. In the present setting each individual has a…
We consider a SIR model with temporary immunity and time dependent transmission rate. We assume time dependent vaccination which confers the same immunity as natural infection. We study two types of vaccination strategies: i) optimal…
We consider a SIR model with vaccination strategy on a sparse configuration model random graph. We show the convergence of the system when the number of nodes grows and characterize the scaling limits. Then, we prove the existence of…
We study the spread of an SIRS-type epidemic with vaccination on network. Starting from an exact Markov description of the model, we investigate the mean epidemic lifetime by providing a sufficient condition for fast extinction that depends…
Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that…