摘要
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 1and satisfy certain conditions,the viruses continue to prevail and will become a local disease.
出处
《中山大学学报（自然科学版）》
CAS
CSCD
北大核心
2016年第3期47-51,共5页
Acta Scientiarum Naturalium Universitatis Sunyatseni
基金
国家自然科学基金资助项目(11371306)
福建省教育厅自然科学基金资助项目(JA13370
JB13269)
福建师范大学闽南科技学院青年骨干教师重点培养对象资助项目(mkq201006)
关键词
SQIR传染病模型
有界性
非负平衡点
全局渐近稳定性
SIQR epidemic model
boundedness
nonnegative equilibrium point
global asymptotic stability
