An SEIR Epidemic Model with Profitless Latent Period Time Delay and Pulse Vaccination

In this paper, we formulate a robust SEIR epidemic disease model with a profitless delay and nonlinear incidence, and analyze the dynamics behaviors of the model under pulse vaccination. By use of 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 when some parameters of the model are under appropriate conditions. Using the theory on delay functional and impulsive differential equation, we obtain sufficient condition with time delay for the permanence of the system, and prove that time delays, pulse vaccination and nonlinear incidence can bring obvious effects on the dynamics behaviors of the model. Our results indicate that the delay is “profitless”. The theoretical results are confirmed by numerical simulations.