1. 福建师范大学闽南科技学院,福建,泉州,362332
2.
纸质出版日期:2016,
网络出版日期:2016-5-25,
扫 描 看 全 文
傅金波, 陈兰荪. 基于生态环境和阶段结构的SIQR传染病模型的全局稳定性[J]. 中山大学学报(自然科学版)(中英文), 2016,55(3):47-51.
FU Jinbo, CHEN Lansun. Global stability in a SQIR epidemic model with ecological environment and stage structure[J]. Acta Scientiarum Naturalium Universitatis SunYatseni, 2016,55(3):47-51.
根据传染病动力学原理建立了一类基于生态环境和阶段结构的SIQR传染病模型,将种群分为成年和幼年两个阶段,而且病毒仅在成年种群传播,而成年种群中的易感群体和幼年种群中接近于成年的活跃群体采取控制策略使之隔离于染病区。利用常微分方程定性与稳定性方法,分析了模型有界性和非负平衡点的存在性,通过构造适当的Lyapunov函数和极限系统理论,获得了平凡平衡点、无病平衡点和地方病平衡点全局渐近稳定的充分条件。 研究结果表明:当基本再生数小于等于1时,所有种群趋于灭绝;当基本再生数大于1并满足一定条件时,病毒将被清除;当病毒主导再生数大于1并满足一定条件时,病毒持续流行并将成为一种地方病。
By using epidemic dynamic theory
a class of SQIR epidemic model with ecological environment and stage-structure is established
in which the population is divided into two life stages-mature and immature
and the viruses spread only in adult population
while the susceptible group of adult population and active sub adult group of immature population are insulated from the infected area by adopting control strategy. By means of qualitative method and stability method of ordinary differential equations
the boundedness of the model and the existence of nonnegative equilibrium point are analyzed. By constructing proper Lyapunov function and limit system theory
sufficient conditions of the global asymptotic stability of the trivial equilibrium point
disease-free equilibrium point and endemic equilibrium point are obtained. The results show that: when the basic reproduction number is less than or equal to 1
all populations tend to be extinct; when the basic reproduction number is greater than 1 and satisfy certain conditions
the viruses will be cleared; when the dominant regeneration number of the viruses is greater than 1 and satisfy certain conditions
the viruses continue to prevail and will become a local disease.
SQIR传染病模型有界性非负平衡点全局渐近稳定性
SIQR epidemic modelboundednessnonnegative equilibrium pointglobal asymptotic stability
0
浏览量
251
下载量
0
CSCD
关联资源
相关文章
相关作者
相关机构