Gao Shujing, Chen Lansun, Nieto Juan J, Torres Angela
Department of Mathematics and Computer Science, Gannan Normal College, Ganzhou 341000, PR China.
Vaccine. 2006 Aug 28;24(35-36):6037-45. doi: 10.1016/j.vaccine.2006.05.018. Epub 2006 Jun 5.
Pulse vaccination is an important strategy for the elimination of infectious diseases. An SEIRS epidemic model with time delays and pulse vaccination is formulated in this paper. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic system and prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger than theta*. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than theta*. The permanence of the model is investigated analytically. Our results indicate that a long latent period of the disease is sufficient condition for the extinction of the disease.
脉冲疫苗接种是消除传染病的一项重要策略。本文建立了一个具有时滞和脉冲疫苗接种的SEIRS传染病模型。利用频闪映射确定的离散动力系统，我们得到了脉冲传染病系统的精确无感染周期解，并证明了当疫苗接种率大于θ时，无感染周期解是全局吸引的。此外，我们表明当疫苗接种率小于θ时，疾病是一致持续存在的。对该模型的持久性进行了分析研究。我们的结果表明，疾病的长潜伏期是疾病灭绝的充分条件。
