具有垂直传染的年龄结构SEIR流行病模型的稳定性

本文讨论了一类具有垂直传染的年龄结构SEIR 流行病模型,运用有界线性算子半群理论证明了模型本身非负解的存在唯一性.运用微分方程及积分方程中的理论和方法, 研究了该模型平衡点的稳定性,得到了无病平衡点与地方病平衡点的稳定性条件.     

一类具有垂直传染与脉冲免疫的SEIR传染病模型的全局分析

考虑了一个具有垂直传染与积分时滞的SEIR传染病动力学模型.分析了该模型在脉冲免疫接种条件下的动力学行为,获得了传染病灭绝的充分条件,进而运用脉冲时滞泛函微分方程理论,获得了含有时滞的系统持久性的充分条件,并且证明了积分时滞与脉冲免疫能对模型的动力学行为产生显著的影响.     

GLOBAL STABILITY OF AN SVIR EPIDEMIC MODEL WITH VACCINATION

In this paper, an SIR epidemic model with vaccination for both the newborns and susceptibles is investigated, where it is assumed that the vaccinated individuals have the temporary immunity. The basic reproduction number determining the extinction or persistence of the infection is found. By constructing a Lyapunov function, it is proved that the disease free equilibrium is globally stable when the basic reproduction number is less than or equal to one, and that the endemic equilibrium is globally stable wh...     

GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS

In this article, an SIRS epidemic model spread by vectors (mosquitoes) which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point (if it exists) is globally stable with a respect "weak delay". Some known results are generalized.     

ANALYSIS OF A SUSCEPTIBLE-EXPOSED-INFECTED EPIDEMIC MODEL WITH RANDOM PERTURBATION AND VARYING POPULATION SIZE

In this paper, we study a type of susceptible-exposed-infected (SEI) epidemic model with varying population size and introduce the random perturbation of the constant contact rate into the SEI epidemic model due to the universal existence of fluctuations. Under some moderate conditions, the density of the exposed and the infected individuals exponentially approaches zero almost surely are derived. Furthermore, the stochastic SEI epidemic model admits a stationary distribution around the endemic equilibrium, and the solution is ergodic. Some numerical simulations are carried out to demonstrate the efficiency of the main results.     

GLOBAL DYNAMICS OF A PREDATOR-PREY MODEL WITH PREY REFUGE AND DISEASE

In this paper, we study a predator-prey model with prey refuge and disease. We study the local asymptotic stability of the equilibriums of the system. Further, we show that the equilibria are globally asymptotically stable if the equilibria are locally asymptotically stable. Some examples are presented to verify our main results. Finally, we give a brief discussion.     

具双时滞的SEIRS传染病模型指数收敛性

本文研究了一类具指数人口统计与结构的SEIRS传染病模型,利用一种新的基于比较原理的分析,获得了无病平衡点局部和全局指数稳定的两个充分条件.     

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 R0 < 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.     

ANALYSIS OF AN SI EPIDEMIC MODEL WITH NONLINEAR TRANSMISSION AND STAGE STRUCTURE

A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.     

带接种疫苗和二次感染的年龄结构MSEIR流行病模型分析

本文讨论带二次感染和接种疫苗的年龄结构MSEIR流行病模型。在常数人口规模的假设下,运用微分方程和积分方程中的理论和方法,得到一个与接种疫苗策略ψ有关的再生数R(ψ)的表达式,证明了当R(ψ)<1时,无病平衡态是局部渐近稳定的;当R(ψ)>1时,无病平衡态是不稳定的,此时存在一个地方病平衡态,并且证明当R(0)<1时,无病平衡态是全局渐近稳定的。     

一类具有常恢复率且总人口变化的SEIS传染病模型的稳定性

This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate.A threshold parameter R is identified.If R≤1,the disease-free equilibrium O is globally stable.IfR>1,there is a unique endemic equilibrium and O is unstable.For two important special cases of bilinear and standard incidence,sufficient conditions for the global stability of this endemic equilibrium are given.The same qualitative results are obtained provided the threshold is more than unity for the corresponding SEIS model with no infectious force in the latent period.Some existing results are extended and improved.     

GLOBAL STABILITY OF SIVS MODEL WITH SATURATION INCIDENCE, INFECTION AGE AND IMPULSIVE VACCINATED RATE

In this paper, an impulsive vaccinated strategy to eradicate SIVS epidemic model is studied. Since infection age is an important factor of epidemic progression, we incorporate the infection age into the model. In this model, we analyze the dynamic behaviors of this model and obtain that there exists an infection-free periodic solution which is globally asymptotically stable under a sufficient condition. Our results indicate that a short period of pulse or a large pulse vaccination rate is the sufficient con...     

A STAGE‐STRUCTURED MODEL WITH TWO TIME‐STEPS FOR ANALYZING THE POPULATION DYNAMICS OF RHEA AMERICANA UNDER VARIABLE ENVIRONMENTAL CONDITIONS

ABSTRACT. The Ñandú or Rhea americana is an autochthonous species perfectly adapted to the pampas environment and only distributed in South America. The species exhibits an unusual breeding system combining polygyny, polyandry, communal nests and exclusive male parental care, which seems to contradict the idea of selfish genes. Our aim has been to construct a mathematical model based on the short term population dynamics of Rhea, living in the wild or in semi‐captivity, and taking into account environmental factors that vary from year to year. Due to the characteristics of its life cycle, it was necessary to develop a model that allows us to differentiate between the survival and fertility rates of each age group and the distinct behavior during breeding and non‐breeding seasons. Therefore, a quarterly differentiated stage‐structured discrete model was needed. Time steps of different lengths are used for modeling chicks or “charos' on the one hand, and juveniles and adults on the other. Environmental variables have been incorporated into the model because they affect the reproductive success of the species. Different scenarios are given as illustrations of the model use. Finally, the possibility of harvesting has been introduced in the model. The model is intended as a first step towards more refined models and systematic data gathering with the purpose of leading the way to a computational tool for risk assessment and decision‐making.