Pulse vaccination of an epidemic model with two parallel infectious stages and time delays()

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 [Formula: see text] the disease will fade out, and if [Formula: see text] , 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 [Formula: see text] and [Formula: see text] 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.