具有隐性感染的登革热模型稳定性分析

李艳,王稳地,周爱蓉,何楠

doi:10.13718/j.cnki.xsxb.2018.05.001

西南师范大学学报(自然科学版)

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具有隐性感染的登革热模型稳定性分析

李艳,王稳地,周爱蓉,何楠. 具有隐性感染的登革热模型稳定性分析[J]. 西南师范大学学报(自然科学版), 2018, 43(5): 1-5. doi: 10.13718/j.cnki.xsxb.2018.05.001

引用本文:

李艳,王稳地,周爱蓉,何楠. 具有隐性感染的登革热模型稳定性分析[J]. 西南师范大学学报(自然科学版), 2018, 43(5): 1-5. doi: 10.13718/j.cnki.xsxb.2018.05.001

LI Yan, WANG Wen-di, ZHOU Ai-rong, HE Nan. Stability Analysis of Dengue Model with Covert Infection[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(5): 1-5. doi: 10.13718/j.cnki.xsxb.2018.05.001

Citation:

LI Yan, WANG Wen-di, ZHOU Ai-rong, HE Nan. Stability Analysis of Dengue Model with Covert Infection[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(5): 1-5. doi: 10.13718/j.cnki.xsxb.2018.05.001

具有隐性感染的登革热模型稳定性分析

李艳,王稳地,周爱蓉,何楠

西南大学数学与统计学院, 重庆 400715

Stability Analysis of Dengue Model with Covert Infection

LI Yan, WANG Wen-di, ZHOU Ai-rong, HE Nan

School of Mathematics and Statistic, Southwest University, Chongqing 400715, China

摘要: 建立了一类具有隐性感染和垂直传播的登革热模型.首先通过构造Lyapunov函数得到了无病平衡点E0是全局渐近稳定的；进一步利用第二加性复合矩阵等理论得到了地方性平衡点E*是全局渐近稳定的条件.
- 隐性感染 /
- Lyapunov函数 /
- 复合矩阵 /
- 全局渐近稳定
Abstract: In this paper, a dengue model with covert infection and vertical transmission has been formulated and studied. First, by constructing a Lyapunov function, the disease-free equilibrium is shown to be globally asymptotically stable. Moreover, by using second additive compound matrices, we obtain the conditions of the globally asymptotical stabilities of the endemice quilibrium.
- covert infection /
- Lyapunov function /
- compound equations /
- global stability .

[1]	张复春.登革热的流行特点及治疗[J].医学与哲学:人文社会医学版,2010,31(18):21-23.
[2]	GUO X,ZHAO T,DONG Y,et al.Survival and Replication of Dengue-2 Virus in Diapausing Eggs of Aedes Blbopictus(Diptera:Culicidae)[J].J Med Entomol,2007,44(3):492-497.
[3]	BOOTS M,GREENMAN J,ROSS D,et al.The Population Dynamical Implications of Covert Infections in Host-Microparasite Interactions[J].J Anim Ecol,2003,72(6):1064-1072.
[4]	DRIDSSCHE P,WATMOUGH J.Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission[J].J Math Biosci,2002,180(1-2):29-48.
[5]	HALE J,VERDUYN LUNEL S.Introduction to Functional-Dikerential E-Quations[M]//Applied Mathematical Sciences.New York:Springer-Verlag,1993.
[6]	THIEME H R.Persistence under Relaxed Point-Dissipativity (with Application to an Endemic Model)[J].Siam J Math Anal,1993,24(2):407-435.
[7]	马知恩,周义仓,李承治.常微分方程定性与稳定性方法[M].北京:科学出版社,2015.
[8]	LI M Y,MULDOWNEY J S.A Geometric Approach to the Global-Stability Problems[J].Siam J Math Anal,1996,27(4):1070-1083.
[9]	MARTIN R H.Logarithmic Norms and Projections Applied to Linear Differential Systems[J].J Math Anal Appl,1974,45(2):432-454.