带有垂直传染具有年龄结构的接种流行病模型研究

研究了一个带有垂直传染、具有年龄结构的接种ＳＩＳ流行病模型，得到了正平衡解存在性的充分条件．

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

We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attractor, this condition depends on pulse vaccination proportion p. We also obtain the condition of the global asymptotic stability of the solution. The condition shows that large enough pulse vaccination proportion and relatively small interpulse time lead to the eradication of the diseases. Moreover the results of the theoretical study might be instructive to the epidemiology of HIV.

GLOBAL STABILITY OF AN AGE-STRUCTURED SIR EPIDEMIC MODEL WITH PULSE VACCINATION STRATEGY

This paper discusses the application of a pulse vaccination strategy to prevent and control some infectious diseases, which is described by age-structured SIR model in which susceptible and recovered individuals are structured by chronological age, while infected individuals are structured by infection age （duration since infection）. The time dependent disease-free equilibrium is determined, for which an explicit expression exists. The analytical results show that there exists a globally stable infectiomfree situation if the impulsive period T and proportion p satisfy Ro（p,T） 〈 1. Optimal problem is discussed： Pulse vaccination strategy with minimal costs at given R0（p, T） 〈 1.

Global stability of an SEIR epidemic model with vaccination

In this paper, an SEIR epidemic model with vaccination is formulated. The results of our mathematical analysis indicate that the basic reproduction number plays an important role in studying the dynamics of the system. If the basic reproduction number is less than unity, it is shown that the disease-free equilibrium is globally asymptotically stable by comparison arguments. If it is greater than unity, the system is permanent and there is a unique endemic equilibrium. In this case, sufficient conditions are established to guarantee the global stability of the endemic equilibrium by the theory of the compound matrices. Numerical simulations are presented to illustrate the main results.

A MULTI-GROUP SVEIR EPIDEMIC MODEL WITH DISTRIBUTED DELAY AND VACCINATION

In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number R0V which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.

Stability analysis and optimal control of an epidemic model with vaccination

In this paper, we have developed a compartment of epidemic model with vaccination. We have divided the total population into five classes, namely susceptible, exposed, infective, infective in treatment and recovered class. We have discussed about basic properties of the system and found the basic reproduction number （R0） of the system. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium E0 when R0 〈1. When R0 〉1 endemic equilibrium E1 exists and the system becomes locally asymptotically stable at E1 under some conditions. We have also discussed the epidemic model with two controls, vaccination control and treatment control. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of the vaccines and drugs dose. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB. Epidemiological implications of our analytical findings are addressed critically.

TRAVELING WAVES OF AN EPIDEMIC MODEL WITH VACCINATION

An epidemic model with vaccination and spatial diffusion is studied. By analyzing the corresponding characteristic equations, the local stability of each of feasible steady states to this model is discussed. The existence of a traveling wave solution is established by using the technique of upper and lower solutions and Schauder＇s fixed point theorem. Numerical simulations are carried out to illustrate the main results.

A delayed SEIRS epidemic model with impulsive vaccination and nonlinear incidence rate

In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impul- sive vaccination is investigated. In vaccination strategy, we perform impulsive vaccina- tion of newborn infants. Using the discrete dynamic system determined by stroboscopic map, we obtain an infection-free periodic solution and establish conditions, on which the solution is globally attractive. We also conclude that the disease is permanent if the parameters of the model satisfy appropriate conditions. Finally, we illustrate the effec- tiveness of our theorems with numerical simulation. The results obtained in this paper are a good extension of the results obtained in [J. Hou and Z. Teng, Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rate, Math. Comput, Simulat. 79 （2009） 3038 3054] to the corresponding delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination.