GLOBAL ANALYSIS OF SIS EPIDEMIC MODEL WITH A SIMPLE VACCINATION AND MULTIPLE ENDEMIC EQUILIBRIA

An SIS epidemic model with a simple vaccination is investigated in this article, The efficiency of vaccine, the disease-related death rate and population dynamics are also considered in this model. The authors find two threshold R0 and Rc （Rc may not exist）. There is a unique endemic equilibrium for R0 〉 1 or Rc = R0; there are two endemic equilibria for Rc 〈 R0 〈 1; and there is no endemic equilibrium for Rn 〈 Rc 〈 1. When Rc exists, there is a backward bifurcation from the disease-free equilibrium for R0 = 1. They analyze the stability of equilibria and obtain the globally dynamic behaviors of the model. The results acquired in this article show that an accurate estimation of the efficiency of vaccine is necessary to prevent and controll the spread of disease.

Epidemic spreading on networks with vaccination

In this paper, a new susceptible-infected-susceptible （SIS） model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns （the recovered individuals have or have not immunity） on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine＇s effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.

Vaccination effect on a stochastic epidemic model with healing and relapse

In this work,we consider a stochastic epidemic model with vaccination,healing and relapse.We prove the existence and the uniqueness of the positive solution.We establish sufficient conditions for the extinction and the persistence in mean of the stochastic system.Moreover,we also establish sufficient conditions for the existence of ergodic stationary distribution to the model,which reveals that the infectious disease will persist.The graphical illustrations of the approximate solutions of the stochastic epidemic model have been performed.

A Stochastic SIVS Epidemic Model Based on Birth and Death Process

A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.

The Effect of State-Dependent Control for an SIRS Epidemic Model with Varying Total Population

Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.

AN SEIRS EPIDEMIC MODEL WITH TWO DELAYS AND PULSE VACCINATION

脉搏种痘是有效、重要的策略根除传染疾病。作者与二延期和脉搏种痘调查一个 SEIRS 流行模型。由使用频闪观测仪的地图决定的分离动态系统，作者获得如果，传染人口灭绝 R Δ【 1，并且传染人口是一致地坚持的如果 R Δ】 1。结果显示脉搏种痘或大脉搏种痘率的一个短时期是一个足够的条件根除疾病。

GLOBAL ASYMPTOTIC STABLE ERADICATION FOR THE SIV EPIDEMIC MODEL WITH IMPULSIVE VACCINATION AND INFECTION-AGE

我们学习脉搏种痘策略的申请根除在潜伏期有传染海角的慢慢地进行的疾病。我们导出根除答案是一个全球引起注意的人的在条件，这个条件取决于脉搏种痘比例 p。我们也获得答案的全球 asymptotic 稳定性的条件。Thecondition 显示出那个足够大的脉搏种痘比例并且相对小内部脉搏时间导致疾病的根除。而且理论学习的结果可能对 HIV 的传染病学有启发性。

An Improved Method to an Impulsive and Delayed Discretized Model

In this paper, a discretized SIR model with pulse vaccination and time delay is proposed. We introduce two thresholds R* and R*, and further prove that the disease-free periodic solution is globally attractive if R* is less than unit and the disease can invade if R* is larger than unit. The numerical simulations not only illustrate the validity of our main results, but also exhibit bifurcation phenomenon. Our result shows that decreasing infection rate can put off the disease outbreak and reduce the number of infected individuals.

基于疫苗接种的SEIHRVI传染病模型分析与最优控制

为研究疫苗接种对控制传染病的影响,建立了具有标准发生率的传染病模型。通过推导得出模型的基本再生数,给出地方病平衡点的存在条件。借助构造Lyapunov函数证明了平衡点的全局稳定性。应用Pontryagin最大值原理分析了最优控制问题,得出最优控制策略。结果表明:提高疫苗接种率和效力能有效控制疾病传播;注意自我保护,及时接种以及重视治疗一定程度上可减小疾病爆发的规模。

Analysis of an Age Structured SEIRS Epidemic Model with Varying Total Population Size and Vaccination

This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction number in the presence of vaccine ( is the exponent of growth of total population), and show that the infection-free steady state is linearly stable if and unstable if , then we apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategy can be either one- or two-age strategies.

Dynamical Behavior of SEIR-SVS Epidemic Models with Nonlinear Incidence and Vaccination

For some infectious diseases such as mumps,HBV,there is evidence showing that vaccinated individuals always lose their immunity at different rates depending on the inoculation time.In this paper,we propose an age-structured epidemic model using a step function to describe the rate at which vaccinated individuals lose immunity and reduce the age-structured epidemic model to the delay differential model.For the age-structured model,we consider the positivity,boundedness,and compactness of the semiflow and study global stability of equilibria by constructing appropriate Lyapunov functionals.Moreover,for the reduced delay differential equation model,we study the existence of the endemic equilibrium and prove the global stability of equilibria.Finally,some numerical simulations are provided to support our theoretical results and a brief discussion is given.

SIVS EPIDEMIC MODELS WITH INFECTION AGE AND NONLINEAR VACCINATION RATE

Vaccination is a very important strategy for the elimination of infectious diseaVaccination is a very important strategy for the elimination of infectious diseases. A SIVS epidemic model with infection age and nonlinear vaccination has been formulated in this paper. Using the theory of differential and integral equation, we show the local asymptotic stability of the infection-free equilibrium and the endemic equilibrium under some assumptions.

A stochastic vaccinated epidemic model incorporating Levy processes with a general awareness-induced incidence

In this paper,we investigate a stochastic vaccinated epidemic model with a general awareness-induced incidence perturbed by Levy noise.First,we show that this model has a unique global positive solution.Therefore,we establish the dynamic behavior of the solution around both disease-free and endemic equilibrium points.Furthermore,when R_(0)>1,we give sufficient conditions for the existence of an ergodic stationary distribution to the model when the jump part in the Levy noise is null.Finally,we present some examples to illustrate the analytical results by numerical simulations.

具有媒体报道的SVIR传染病模型的生存性分析

该文研究了具有Logistic增长和媒体报道的饱和发生率的随机SVIR模型.为了研究模型的动力学性质,首先证明了随机模型全局正解的存在唯一性,其次通过构造合适的李雅普诺夫函数,探究疾病持久和灭绝的充分性条件.研究表明:当R^(s)_(0)>1时,疾病长时间持续存在.当R^(e)_(0)<1时,疾病在流行一段时间后灭绝.最后,通过数值模拟验证了以上结论.

具有马尔科夫切换的SVIR传染病模型的动力学

本文研究在马尔科夫状态下具有Beddington-DeAngeis功能反应发生率的SVIR传染病模型的动力学问题.首先,得到系统具有唯一的全局正解;然后,通过构造恰当的李雅普诺夫函数得到:当R_(0)^(s)> 1时,系统存在平稳分布;当R_(0)^(e)<1时,疾病将会指数灭绝;最后通过数值模拟对本文主要理论的可行性进行验证.