PULSE VACCINATION STRATEGIES IN A INFECTIOUS DISEASE MODEL WITH A NONMONOTONE INCIDENCE RATE AND TWO DELAYS

  • Zhang, Hong (Department of Mathematics, Jiangsu University) ;
  • Chen, Lansun (Institute of Mathematics, Academia Sinica, Department of Applied Mathematics, Dalian University of Technology)
  • Published : 2009.05.31

Abstract

This paper deals with a delayed SEIRS epidemic model with pulse vaccination and crowded incidence rate. Moreover, the case of vertical and horizontal transmission is considered. By using the discrete dynamical system determined by the stroboscopic map, the exact infection-free periodic solution of the SEIRS model is obtained. Further, by employing the comparison arguments, we prove that under the condition that $R_*$ < 1 the infection-free periodic solution is globally attractive, and that under the condition that $R^*$ > 1 the disease is uniformly persistent, which means that after some period of time the disease will become endemic.

Keywords

References

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