PERMANENCE OF A SIRS EPIDEMIC MODEL WITH IMPULSIVE VACCINATION AND DISTRIBUTED DELAYS

In this paper, we consider a SIRS epidemic model with impulsive vaccination and distributed time delays. By the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution to the system. Further, using the comparison theorem, we prove that the infection-free periodic solution is globally attractive under an assumption. A sufficient condition for the permanence of the model is investigated.     

具有接种的确定性和随机SIS流行病模型的全局稳定性

We study the stability of endemic equilibriums of the deterministic and stochastic SIS epidemic models with vaccination. The deterministic SIS epidemic model with vaccination was proposed by Li and Ma(2004), for which some sufficient conditions for the global stability of the endemic equilibrium were given in some earlier works. In this paper, we first prove by Lyapunov function method that the endemic equilibrium of the deterministic model is globally asymptotically stable whenever the basic reproduction number is larger than one. For the stochastic version, we obtain some sufficient conditions for the global stability of the endemic equilibrium by constructing a class of different Lyapunov functions.     

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 t...     

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.     

PERMANENCE AND GLOBAL STABILITY OF POSITIVE SOLUTIONS TO TWO PREDATORSONE PREY SYSTEM WITH A DISCRETE TIME RATIO-DEPENDENT

A three-species ratio-dependent predator-prey discrete model is studied.As a result,sufficient conditions which guarantee the permanence of the model are obtained. In addition,by constructing a suitable Lyapunov function,we derive some sufficient conditions,which ensure that the positive solution of the model is stable and attracts all positive solutions.To illustrate the feasibility of the main results,we introduce an example with corresponding numeric simulations.     

A Sufficient Condition for Rigidity in Extremality of Teichmuller Equivalence Classes by Schwarzian Derivative

The Strebel point is a TeichmOller equivalence class in the Teichmuller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper, we give a sufficient condition in terms of the Schwarzian derivative for a Teichmuller equivalence class of the universal Teichmuller space under which the class is a Strebel point. As an application, we construct a Teichmuller equivalence class that is a Strebel point and that is not an asymptotically conformal class.     

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...     

A Sufficient Condition for Rigidity in Extremality of Teichmller Equivalence Classes by Schwarzian Derivative

The Strebel point is a Teichm ¨uller equivalence class in the Teichm ¨uller space that has a certain rigidity in the extremality of the maximal dilatation. In this paper,we give a sufficient condition in terms of the Schwarzian derivative for a Teichm ¨uller equivalence class of the universal Teichm ¨uller space under which the class is a Strebel point. As an application, we construct a Teichm ¨uller equivalence class that is a Strebel point and that is not an asymptotically conformal class.     

Mi群的一个充分条件

In this note, we give a sufficient condition for Mi-group. In particular, we show that if a finite group G is the semidirect product of two subgroups with coprime orders, in which one is a Sylow tower group and its Sylow subgroups are all abelian, and the other is an Mi-group and all of its proper subgroups are also Mi-groups, then G is an Mi-group.     

A Sufficient Condition for Mi-groups

In this note, we give a sufficient condition for Mi-group. In particular, we show that if a finite group G is the semidirect product of two subgroups with coprime orders, in which one is a Sylow tower group and its Sylow subgroups are all abelian, and the other is an Mi-group and all of its proper subgroups are also Mi-groups, then G is an Mi-group.     

Dynamics of SIS model with saturation incidence,infection age and impulsive birth

In this paper, an impulsive birth and infection age SIS 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 dynamical behaviors of this model and point out that there exists an infection‐free periodic solution that is globally asymptotically stable if R₀<1. When R₁>1, R₂<1, then the disease is permanent. Our results indicate that a large period T of pulse, or a small pulse birth rate p is the sufficient condition for the eradication of the disease. Copyright © 2009 John Wiley & Sons, Ltd.     

Two profitless delays for an SEIRS epidemic disease model with vertical transmission and pulse vaccination

Since the investigation of impulsive delay differential equations is beginning, the literature on delay epidemic models with pulse vaccination is not extensive. In this paper, we propose a new SEIRS epidemic disease model with two profitless delays and vertical transmission, and analyze the dynamics behaviors of the model under pulse vaccination. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ‘infection-free’ periodic solution, further, show that the ‘infection-free’ periodic solution is globally attractive when some parameters of the model are under appropriate conditions. Using a new modeling method, we obtain sufficient condition for the permanence of the epidemic model with pulse vaccination. We show that time delays, pulse vaccination and vertical transmission can bring different effects on the dynamics behaviors of the model by numerical analysis. Our results also show the delays are “profitless”. In this paper, the main feature is to introduce two discrete time delays, vertical transmission and impulse into SEIRS epidemic model and to give pulse vaccination strategies.     

Pulse vaccination on SEIR epidemic model with nonlinear incidence rate

In this paper, we consider an SEIR epidemic model with two time delays and nonlinear incidence rate, and study the dynamical behavior of the model with pulse vaccination. By using the Floquet theorem and comparison theorem, we prove that the infection-free periodic solution is globally attractive when R^*<1, and using a new modelling method, we obtain a sufficient condition for the permanence of the epidemic model with pulse vaccination when R_*>1.     

Epidemic dynamics model with delay and impulsive vaccination control base on variable population

Pulse vaccination is an effective strategy for the elimination of infectious diseases. In this paper, we considered an SEIR epidemic model with delay and impulsive vaccination direct at a variable population and analyzed its dynamic behaviors. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection‐free periodic solution of the impulsive epidemic system, further, prove that the infection‐free periodic solution is globally attractive if the vaccination rate is larger than θ* or the length of latent period of disease is larger than τ* or the length of period of impulsive vaccination is smaller than T*. We also prove that a short latent period of the disease (with τ) or a long period of pulsing (with T) or a small pulse vaccination rate (with θ) is sufficient to bring about the disease is uniformly persistent. Copyright © 2011 John Wiley & Sons, Ltd.     

A delay SIR epidemic model with pulse vaccination and incubation times

In this paper, a new delay SIR epidemic model with pulse vaccination and incubation times is considered. We obtain an infection-free semi-trivial periodic solution and establish the sufficient conditions for the global attractivity of the semi-trivial periodic solution. By use of new computational techniques for impulsive differential equations with delay, we prove that the system is permanent under appropriate conditions. The results show that time delay, pulse vaccination and nonlinear incidence have significant effects on the dynamics behaviors of the model. Our results are illustrated and corroborated with some numerical experiments.     

Global attractivity and permanence of a SVEIR epidemic model with pulse vaccination and time delay

In this study, we propose a new SVEIR epidemic disease model with time delay, and analyze the dynamic behavior of the model under pulse vaccination. Pulse vaccination is an effective strategy for the elimination of infectious disease. Using the discrete dynamical system determined by the stroboscopic map, we obtain an ‘infection-free’ periodic solution. We also show that the ‘infection-free’ periodic solution is globally attractive when some parameters of the model under appropriate conditions. The permanence of the model is investigated analytically. Our results indicate that a large vaccination rate or a short pulse of vaccination or a long latent period is a sufficient condition for the extinction of the disease.     

Global analysis of a delayed epidemic dynamical system with pulse vaccination and nonlinear incidence rate

This study explores the influence of epidemics by numerical simulations and analytical techniques. Pulse vaccination is an effective strategy for the treatment of epidemics. Usually, an infectious disease is discovered after the latent period, H1N1 for instance. The vaccinees (susceptible individuals who have started the vaccination process) are different from both susceptible and recovered individuals. So we put forward a SVEIRS epidemic model with two time delays and nonlinear incidence rate, and analyze the dynamical behavior of the model under pulse vaccination. The global attractivity of ‘infection-free’ periodic solution and the existence, uniqueness, permanence of the endemic periodic solution are investigated. We obtain sufficient condition for the permanence of the epidemic model with pulse vaccination. The main feature of this study is to introduce two discrete time delays and impulse into SVEIRS epidemic model and to give pulse vaccination strategies.     

Global attractivity and permanence of a delayed SVEIR epidemic model with pulse vaccination and saturation incidence

In this study, we formulate and analyze a new SVEIR epidemic disease model with time delay and saturation incidence, and analyze the dynamic behavior of the model under pulse vaccination. Using the discrete dynamical system determined by the stroboscopic map, we obtain an ‘infection-free’ periodic solution, further, show that the ‘infection-free’ periodic solution is globally attractive for some parameters of the model under appropriate conditions. The permanence of the model is investigated analytically. By computer simulation it is concluded that a large vaccination rate or a short pulse of vaccination or a long latent period are each a sufficient condition for the extinction of the disease.     

Global stability for a multi-group SIRS epidemic model with varying population sizes

In this paper, by extending well-known Lyapunov function techniques to SIRS epidemic models, we establish sufficient conditions for the global stability of an endemic equilibrium of a multi-group SIRS epidemic model with varying population sizes which has cross patch infection between different groups. Our proof no longer needs such a grouping technique by graph theory commonly used to analyze the multi-group SIR models.     

基于脉冲控制的害虫管理数学模型研究

研究一类害虫管理SI传染病模型,考虑脉冲投放病虫和人工捕杀相结合,得到系统的灭绝周期解,给出此周期解的全局吸引性,并获得了系统一致持续生存的条件.给出了害虫管理综合防治策略.