摘要
通过假设捕食系统中疾病只在食饵种群中传播,被传染的易惑者经过一段潜伏期后才具有传染性,潜伏者与染病者均具有垂直传播能力,染病者恢复后对该病不具有终身免疫力,建立了一类具有垂直传播的SEIRS捕食传染病模型,运用极限系统理论,分两种情形讨论了系统平衡点的存在性及局部稳定性,利用Lyapunov函数和二次复合矩阵等方法,得到了平衡点全局渐近稳定的条件.
By assuming that disease only exists in the prey species,a susceptible individual infected by infective becomes infectious individual after a latent period, the infectives and the latent individuals have the ability of vertical transmission,and the infectives can be cured but the recovered have temporary immunity, an SEIRS predator-prey epidemic model with vertical transmission is investigated. Through the limiting system theory, the existence and the local stability of the equilibria for two cases are discussed. By constructing the liapunov function and using the second additive compound matrix, the sufficient and necessary conditions of the global stability of the boundary equilibria and the sufficient condition of the global stability of the co- existing equilibrium are obtained.
出处
《生物数学学报》
CSCD
北大核心
2010年第1期104-112,共9页
Journal of Biomathematics
基金
国家自然科学基金(10671209)项目资助
陕西省自然科学基金(SJ08-ZT13)项目资助
关键词
垂直传播
潜伏期
捕食系统
传染病模型
平衡点
稳定性
Vertical transmission
Latent period
Predator-prey system
Epidemic model
Equilibrium
stability
