具有阶段结构、时滞和接种的幼年染病单种群模型的稳定性

Stability of a delayed stage-structured single-species model with disease in infancy and vaccination

研究了一类具有阶段结构、时滞和接种的幼年染病单种群模型的稳定性.应用极限系统理论和构造Liapunov函数,得到系统各类平衡点全局渐近稳定的充分条件.结果表明:在一定的接种率下,且整个种群的生育率位于某一区间时,最终疾病将趋于灭绝;当种群的生育率高于某一阈值时,疾病将最终成为地方病.

A delayed stage-structured single-species model with disease in infancy and vaccination is investigated. Using limit system theorem and constructing Liapunov function, the sufficient conditions for the global asymptotically stability of the positive equilibrium point and the infection-free equilibrium point are obtained. The results show that in the certain immunization coverage rate, the disease will eventually become extinct when the birth rate of the species is located in an interval,and when the birth rate is large than a threshold, the disease will eventually become an endemic.