含有接种和非线性传染力的流行病模型的稳定性研究
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摘要
研究一类含有接种和非线性传染力的SEIR流行病模型,通过分析得到了各类平衡点存在的阈值条件.利用Liapunove函数、Lasalle不变集原理、Hurwith判据证明了当基本再生数R0!1时,无病平衡点是全局渐近稳定的;当时,此模型存在两个平衡点,其中无病平衡点是不稳定的,利用Hurwitz判别法证明了地方病平衡点的局部渐近稳定性.最后对模型进行数据模拟,分析了接种对疾病流行的影响,并对文中的主要结论进行了验证.
class of SEIR infectious disease model with inoculation is studed,and obtains the threshold condition of the existence of various equilibrium points. By using Liapunove function,Lasalle invariance principle,Hurwith criterion is proved when the basic reproduction number is less than one,the disease-free equilibrium is globally asymptotically stable; when the basic reproduction number is greater than one,this model has two equilibria,the disease-free equilibrium is unstable,discriminant analysis proved the local asymptotic stability of the equilibrium point local disease by Hurwitz,further using the theory of matrix composite track stability and global asymptotic stability of the endemic equilibrium is proved.Finally,the model is simulated,and the effect of vaccination on the epidemic is analyzed,and the main conclusions are verified in this paper.
class of SEIR infectious disease model with inoculation is studed,and obtains the threshold condition of the existence of various equilibrium points. By using Liapunove function,Lasalle invariance principle,Hurwith criterion is proved when the basic reproduction number is less than one,the disease-free equilibrium is globally asymptotically stable; when the basic reproduction number is greater than one,this model has two equilibria,the disease-free equilibrium is unstable,discriminant analysis proved the local asymptotic stability of the equilibrium point local disease by Hurwitz,further using the theory of matrix composite track stability and global asymptotic stability of the endemic equilibrium is proved.Finally,the model is simulated,and the effect of vaccination on the epidemic is analyzed,and the main conclusions are verified in this paper.
引文
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[3] Xu min,Hu liang jian.Global Asymptotical Stability ofan SEIR Model with Random Perturbation[J]. Journalof Dong hua University(English Edition),2014,31(2):152-154.
[4]童姗姗,牛玉俊.具有媒体效应和接种的传染病模型的稳定性分析[J].吉林化工学院学报,2015(11):77-79.
[5]王改霞,刘纪轩,李学志,等.年龄结构SIQRS传染病模型稳定性及接种决策[J].应用数学,2018,31(2):392-399.
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[15]辛京奇,王文娟.一类带有接种的SIR传染病模型的全局分析[J].数学的实践与认识,2007,37(20):71-76.
[16]朱慧,熊佐亮,王娓.预防接种下具有非线性传染率的SEIR传染病模型的全局分析[J].南昌大学学报:理学版,2009,33(2):113-117.
[17]朱焕,李冬梅,刘伟华,等.一类具有连续接种的时滞SEIR传染病模型[J].哈尔滨理工大学学报,2013,18(5):123-128.
[18]王娟,王燕,李学志.具有接种疫苗和重复感染的SEIR传染病模型的分析[J].数学的实践与认识,2014,44(15):317-322.
[19]廖书,杨炜明.同时含有预防接种和水源处理的霍乱时滞模型分析[J].重庆工商大学学报(自然科学版),2018(2):48-53.
[20]周艳丽,张卫国.具有非线性传染率的SIQS传染病模型定性分析和数值模拟[J].数学的实践与认识,2013,43(19):281-286.
[2]王玉杰,奚晓军.HIV模型的稳定性与Hopf分支问题研究[J].吉林化工学院学报,2017(11):90-94.
[3] Xu min,Hu liang jian.Global Asymptotical Stability ofan SEIR Model with Random Perturbation[J]. Journalof Dong hua University(English Edition),2014,31(2):152-154.
[4]童姗姗,牛玉俊.具有媒体效应和接种的传染病模型的稳定性分析[J].吉林化工学院学报,2015(11):77-79.
[5]王改霞,刘纪轩,李学志,等.年龄结构SIQRS传染病模型稳定性及接种决策[J].应用数学,2018,31(2):392-399.
[6]周艳丽,濮桂萍,沈新娣,等.带有接种的随机SIS传染病模型研究[J].上海理工大学学报,2017,39(6):528-531.
[7]霍海峰,邹明轩.一类具有接种和隔离治疗的结核病模型的稳定性[J].兰州理工大学学报,2016,42(3):150-154.
[8]单秀丽,刘会民.不同控制策略对一类SIQR传染病模型的影响[J].中北大学学报(自然科学版),2014(2):97-100.
[9]庞伟娟,胡志兴,王辉,等.一类具有饱和传染率且带有潜伏期和接种期的SVEIR模型的研究[J].工程数学学报,2014(5):664-674.
[10]吴梦媛,孙法国,陈瑶,等.一类具有接种和治疗的传染病模型动力学分析[J].哈尔滨商业大学学报(自然科学版),2017,33(6):738-743.
[11]侯新华,王菲.对接种条件下时滞双病毒感染模型的稳定性分析[J].湖南师范大学自然科学学报,2013,36(1):5-11.
[12]王烈,陈斯养.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[J].陕西师范大学学报(自然科学版),2013,41(1):15-19.
[13]杨文川.基于斑块环境下SIS传染病模型局部稳定性分析[J].重庆工商大学学报(自然科学版),2015,32(3):21-24.
[14] Xu min,Hu liang jian.Persistence in a Stochastic SEIRModel with Constant Immigration in Incubation Period[J].Journal of Dong hua University(English Edition),2016,33(4):649-651.
[15]辛京奇,王文娟.一类带有接种的SIR传染病模型的全局分析[J].数学的实践与认识,2007,37(20):71-76.
[16]朱慧,熊佐亮,王娓.预防接种下具有非线性传染率的SEIR传染病模型的全局分析[J].南昌大学学报:理学版,2009,33(2):113-117.
[17]朱焕,李冬梅,刘伟华,等.一类具有连续接种的时滞SEIR传染病模型[J].哈尔滨理工大学学报,2013,18(5):123-128.
[18]王娟,王燕,李学志.具有接种疫苗和重复感染的SEIR传染病模型的分析[J].数学的实践与认识,2014,44(15):317-322.
[19]廖书,杨炜明.同时含有预防接种和水源处理的霍乱时滞模型分析[J].重庆工商大学学报(自然科学版),2018(2):48-53.
[20]周艳丽,张卫国.具有非线性传染率的SIQS传染病模型定性分析和数值模拟[J].数学的实践与认识,2013,43(19):281-286.