摘要
考虑因病死亡因素影响的情况下,讨论一类具有免疫接种且有效接触率依赖于总人口变化的SIR和SIS组合传染病模型.给出了决定疾病灭绝和持续生存的基本再生数R_0的具体表达式,并且在一定条件下,利用微分方程稳定性理论,证明了平衡点的存在性以及渐近稳定性.
In this paper, by considering the factors of death due to illness, we discussed a class of the combination of SIR and SIS infectious disease model with vaccination and effective immunization rate relative to the total population. We gave the explicit expression of the basic reproductive number R0 which decide the disease is extinction or is persistence, and under certain conditions, by using the stability theory of differential equations, we proved the existence of the equilibrium point and asymptotic stability.
出处
《新疆大学学报（自然科学版）》
CAS
2012年第3期293-298,共6页
Journal of Xinjiang University(Natural Science Edition)
基金
国家自然科学基金(10961022
10901130)
新疆维吾尔自治区自然科学基金(2010211A07)
关键词
传染病模型
平衡点
基本再生数
渐近稳定性
infectious disease model
equilibrium point
basic reproductive number
asymptotic stability
