1. Pulse vaccination of an epidemic model with two parallel infectious stages and time delays
- Author
-
Li Shuping, Pei Yongzhen, Zhong Min, and Gao Shujing
- Subjects
0301 basic medicine ,Numerical Analysis ,Time delays ,General Computer Science ,Applied Mathematics ,01 natural sciences ,Stability (probability) ,Article ,Permanence ,010305 fluids & plasmas ,Theoretical Computer Science ,03 medical and health sciences ,030104 developmental biology ,Pulse vaccination ,Parallel infectious stages ,Modeling and Simulation ,0103 physical sciences ,Applied mathematics ,Epidemic model ,Stability ,Time delay ,Mathematics - Abstract
An epidemic model with two parallel infectious stages and time delays and pulse vaccination is proposed. We introduce four thresholds and further obtain the conditions that the disease will be extinct or not. Corollaries show that under condition that θ > max { θ ∗ 1 , θ ∗ 2 } the disease will fade out, and if θ min { θ 1 ∗ , θ 2 ∗ } , the disease will be endemic. Our results indicate that a larger pulse vaccination rate will lead to the eradication of a disease. Furthermore, two thresholds ℜ ∗ 1 and ℜ ∗ 2 show that the diversity of the contagiousness affects the basic properties of these models. In addition, numerical results indicate that the probability for an infected individual to enter different infective compartments greatly affects two infective compartments.
- Published
- 2012