Global dynamics behaviors for new delay SEIR epidemic disease model with vertical transmission and pulse vaccination

A robust SEIR epidemic disease model with a profitless delay and vertical transmission is formulated, and the dynamics behaviors of the model under pulse vaccination are analyzed. By use of the discrete dynamical system determined by the stroboscopic map, an ‘infection-free＇ periodic solution is obtained, further, it is shown that the ‘infection-free＇ periodic solution is globally attractive when some parameters of the model are under appropriate conditions. Using the theory on delay functional and impulsive differential equation, the sufficient condition with time delay for the permanence of the system is obtained, and it is proved that time delays, pulse vaccination and vertical transmission can bring obvious effects on the dynamics behaviors of the model. The results indicate that the delay is ‘profitless’.

An improved ISR-WV rumor propagation model based on multichannels with time delay and pulse vaccination

The rapid development of the Internet has broadened the channels of dissemination of information,it has also led to the rapid and widespread propagation of rumors,which can have a serious negative impact socially.In this paper,an improved ISR-WV rumor propagation model integrating multichannels is proposed by considering the system’s time delay,and the influence of different channels of propagation on the dynamic process is further analyzed.Moreover,the basic reproduction number R0,rumor-free equilibrium,and rumor-prevailing equilibrium,as well as their stability,are deduced.Then,an optimal control problem with pulse vaccination is designed.Finally,the validity of the model and theoretical results is verified by numerical simulations and a practical application.The results show that the rumor propagation threshold R0 is more sensitive to the rate of the propagation of the information base channel.The shorter the thinking timeτ_(1)required for the ignorant to react after obtaining the information,the larger the final scale of propagation.Under this condition,the time delayτ_(2)spent by a spreader in producing a video is negatively related to the final scale of the propagation;conversely,a longerτ_(1)implies that the person tends to more cognizant,which can suppress the spread of rumors.Under this condition,τ_(2)has little effect on the final scale of propagation.In addition,the results also prove that timely implementation of the pulse vaccination control strategy of popular science education can effectively control the propagation of rumors and reduce their negative impact.

AN SEIRS EPIDEMIC MODEL WITH TWO DELAYS AND PULSE VACCINATION

Pulse vaccination is an effective and important strategy to eradicate an infectious disease. The authors investigate an SEIRS epidemic model with two delays and pulse vaccination. By using the discrete dynamical system determined by stroboscopic map, the authors obtain that the infectious population dies out if R△ 〈 1, and the infectious population is uniformly persistent if R^△ 〉 1. The results indicate that a short period of pulse vaccination or a large pulse vaccination rate is a sufficient condition to eradicate the disease.

Mathematical analysis of pulse vaccination in controlling the dynamics of measles transmission

Although the incidence of measles has been significantly reduced through vaccination,it remains an important public health problem.In this paper,a measles model with pulse vaccination is formulated to investigate the influential pulse vaccination on the period of time for the extinction of the disease.The threshold value of the formulated model,called the control reproduction number and denoted by R^(*),is derived.It is found that the disease-free periodic solution of the model exists and is globally attractivity whenever R^(*)<1 in the sense that measles is eliminated.If R^(*)>1,the positive solution of the model exists and is permanent which indicates the disease persists in the community.Theoretical conditions for disease eradication under various constraints are given.The effect of pulse vaccination is explored using data from Thailand.The results obtained can guide policymakers in deciding on the optimal scheduling in order to achieve the strategic plan of measles elimination by vaccination.

Immunotherapeutic effects of dendiritic cells vaccine pulsed with tumor cell lysate in mice with pancreatic carcinoma

Objective To observe the immunotherapeutic effects of dendritic cells vaccine pulsed with tumor cell lystate on mice with pancreatic carcinoma. Methods Dendritic cells (MTSC4) were pulsed with tumor cells lysate. The immune preventative and immnotherapeutic effects of DC vaccines on mice with pancreatic carcinoma were assessed. Results After vaccination of the DC vaccines,mice remained tumor-free for at least 25 days in DCs vaccines group,but in other groups the subcutaneous implantation tumorigenesis were found beginning 3 to 9 days. CTL stimulated by DC vaccines effected cytolytic activity against pancreatic carcinoma cells. The survival period was obviously prolonged in DCs vaccines group (56 ±9)d than in other groups P【0.01) and tumors (1.4 ±0.8)g in DCs vaccines group were significantly smaller than that in other groups (P 【 0. 05). Conclusion Tumor cell lysate-pulsed dendrtic cells vaccines can induce a specific and effective immune response against pancreatic carcinoma cell implanted in mice.

Location of emergency rescue center based on SIR epidemiological model

In view of the pressure time of emergency rescue against the infectious diseases,a mathematical model to optimize the location of emergency rescue centers is proposed.The model takes full account of the spread function of infectious diseases,the cycle of pulse vaccination,the distance between the demand area and the emergency rescue centers,as well as the building and maintenance cost for the emergency rescue center,and so on.At the same time,the model integrates the traditional location selection models which are the biggest cover model,the p-center model and the p-median model,and it embodies the principles of fairness and efficiency for the emergency center location.Finally,a computation of an example arising from practice provides satisfactory results.

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.