A Delayed Epidemic Model with Pulse Vaccination

A delayed SEIRS epidemic model with pulse vaccination and nonlinear incidence rate is proposed. We analyze the dynamical behaviors of this model and point out that there exists an infection-free periodic solution which is globally attractive if 𝑅1l1, 𝑅2g1, and the disease is permanent. Our results indicate that a short period of pulse or a large pulse vaccination rate is the sufficient condition for the eradication of the disease. The main feature of this paper is to introduce time delay and impulse into SEIRS model and give pulse vaccination strategies.

[1]  Y. Iwasa,et al.  Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models , 1986, Journal of mathematical biology.

[2]  Global attractivity for certain impulsive delay differential equations , 2003 .

[3]  Wendi Wang,et al.  Global behavior of an SEIRS epidemic model with time delays , 2002, Appl. Math. Lett..

[4]  Lansun Chen,et al.  Two profitless delays for the SEIRS epidemic disease model with nonlinear incidence and pulse vaccination , 2007, Appl. Math. Comput..

[5]  Zhen Jin,et al.  GLOBAL STABILITY OF A SEIR EPIDEMIC MODEL WITH INFECTIOUS FORCE IN LATENT, INFECTED AND IMMUNE PERIOD , 2005 .

[6]  Herbert W. Hethcote,et al.  The Mathematics of Infectious Diseases , 2000, SIAM Rev..

[7]  Juan J. Nieto,et al.  Existence and global attractivity of positiveperiodic solution of periodic single-species impulsive Lotka-Volterra systems , 2004, Math. Comput. Model..

[8]  K. L. Cooke,et al.  Analysis of an SEIRS epidemic model with two delays , 1996, Journal of mathematical biology.

[9]  Guoping Pang,et al.  A delayed SIRS epidemic model with pulse vaccination , 2007 .

[10]  Sanyi Tang,et al.  The effect of seasonal harvesting on stage-structured population models , 2004, Journal of mathematical biology.

[11]  B. Shulgin,et al.  Pulse vaccination strategy in the SIR epidemic model , 1998, Bulletin of mathematical biology.

[12]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.