Dynamic behavior of a delayed impulsive SEIRS model in epidemiology

Abstract

A delayed SEIRS epidemic model with pulse vaccination is investigated. Using Krasnoselskii's fixed-point theorem, the infection-free periodic solution is obtained. Some new threshold values R1, R2 and R 3 are obtained for dynamic behavior of the solutions. We point out, if R1 < 1, the infectious population disappear, i.e., the disease dies out, while if R2 > 1 or R3 > 1, the infectious permanent, the infectious population will ultimately remain above a positive level. An explicit formula is obtained by which the eventual lower bound of infectious individuals can be computed when R2 > 1. Our results indicate that a large pulse vaccination rate will have some active effects to prevent or curtail the spread of the disease. Furthermore, we only proved the existence of R3 based upon some abstract theories. Copyright © 2008 Rocky Mountain Mathematics Consortium.