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

Abstract

In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination is investigated. In vaccination strategy, we perform impulsive vaccination 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 effectiveness 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.

Global dynamics of a nonautonomous SEIRS epidemic model with vaccination and nonlinear incidence

“…Therefore, SEIRS epidemic model is further developed to characterize such diseases. Presently, we see that there is quite a few works on the autonomous SEIRS epidemic models (see previous works 21–30 and the references cited therein).…”

On the stability of an SEIR epidemic model with distributed time-delay and a general class of feedback vaccination rules

“…Feedback and impulsive vaccination laws and optimal vaccination laws have been also proposed. See, [23][24][25] and references therein. The relevance of delays in the study of vaccination controls, neural networks and stochastic control systems has been recently discussed in [5,26,27] and references therein.…”

Impulsive Vaccination SEIR Model with Nonlinear Incidence Rate and Time Delay

“…By constructing an appropriate Lyapunov function, the global attractability of the unique positive periodic solution has been discussed in [15] for the pulse predator-prey system with distributed delay and proliferated. Also, by using the comparison principle of impulsive differential equations, the influence from the time delay, the pulse vaccination, and the other factors on the nature of the model has been tackled in [16,17].…”