|Table of Contents|

A class of nonlinear dynamic system for epidemic virus transmission(PDF)

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
2019年03期
Page:
286-291
Research Field:
Publishing date:

Info

Title:
A class of nonlinear dynamic system for epidemic virus transmission
Author(s):
Xu Jianzhong1Mo Jiaqi2
1.Department of Electronics and Information Engineering,Bozhou University,Bozhou 236800,China; 2.School of Mathematics and Statistics,Anhui Normal University,Wuhu 241003,China
Keywords:
epidemic virus transmission nonlinear dynamic system functional general variational method dimensionless relative system
PACS:
O175.14
DOI:
-
Abstract:
A class of dynamic system for epidemic contagion region transmission is considered to get the expression of approximate solution for this system. The transmission mode of the human groups in an epidemic contagion region is described. The approximate iteration sequence of the nonlinear dynamic system is got by using the functional general variational method,and its uniform convergence is illustrated. Many times approximate solutions are obtained simply. The availability of this method is verified by taking a simple dimensionless relative system for example.

References:

[1] Griffiths J L,Wrie D,Williams J. An age-structured model for the AIDS epidemic[J]. European J Operational Research,2000,124(1):1-24.
[2]Hyman J M,Li J,Stanley A. The differential infectivity and staged progression models for the transmission of HIV[J]. Mathematical Biosciences,1999,155(1):77-109.
[3]Liu Maoxing,Ruan Yuhua,Han Litao,et al. The summary of dynamic models for HIV transmission[J]. J Biomathematics,2004,19(5):551-560.
[4]De Jager E M,Jiang F. The theory of singular perturbation[M]. Amsterdam,Netherlands:North-Holland Publishing Co.,1996.
[5]Barbu L,Morosanu G. Singularly perturbed boundary-value problems[M]. Basel,Switzerland:Birkhauserm Verlag AG,2007.
[6]D’aprile T,Pistoia A. On the existence of some new positive interior spike solutions to a semilinear Neumann problem[J]. J Differ Eqns,2010,248(3):556-573.
[7]Ei S I,Matuzawa H. The motion of a transition layer for a bistable reaction diffusion equation with heterogeneous environment[J]. Discrete Contin Dyn Syst,2010,26(3):910-921.
[8]Suzuki R. Asymptotic behavior of solutions of a semilinear heat equation with localized reaction[J]. Adv Differ Eqns,2010,15(3-4):283-314.
[9]Deng Shengbing. Mixed interior and boundary bubbling solutions for Neumann problem in R2[J]. J Differ Equations,2012,253(2):727-763.
[10]Mo Jiaqi. Singular perturbation for a class of nonlinear reaction diffusion systems[J]. Science in China,Ser A,1989,32(11):1306-1315.
[11]Mo Jiaqi. Homotopic mapping solving method for gain fluency of a laser pulse amplifier[J]. Science in China,Ser G,2009,39(7):1007-1010.
[12]Mo Jiaqi,Lin Wantao. Asymptotic solution of activator inhibitor systems for nonlinear reaction diffusion equations[J]. J Sys Sci & Complexity,2008,20(1):119-128.
[13]Mo Jiaqi,Lin Shurong. The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation[J]. Chin Phys B,2009,18(9):3628-3631.
[14]Mo Jiaqi. Variational iteration solving method for a class of generalized Boussinesq equation[J]. Chin Phys Lett,2009,26(6):7-9.
[15]莫嘉琪,陈贤峰. 一类广义非线性扰动色散方程孤立波的近似解[J]. 物理学报,2010,50(3):1403-1408.
Mo Jiaqi,Chen Xianfeng. Approximate solution of solitary wave for a class of generalized nonlinear disturbed dispersive equation[J]. Acta Phys Sin,2010,50(3):1403-1408.
[16]Mo Jiaqi,Lin Wantao,Lin Yihua. Asymptotic solution for the El Nino time delay sea-air oscillator model[J]. Chin Phys B,2011,20(7):35-40.
[17]莫嘉琪. 扰动Vakhnenko方程物理模型的行波解[J]. 物理学报,2011,60(9):22-27.
Mo Jiaqi. Travelling wave solution of disturbed Vakhnenko equation for physical model[J]. Acta Phys Sin,2011,60(9):22-27.
[18]莫嘉琪. 一类非线性尘埃等离子体孤波解[J]. 物理学报,2011,60(3):13-16.
Mo Jiaqi. The solution for a class of nonlinear solitary waves in dusty plasma[J]. Acta Phys Sin,2011,60(3):13-16.
[19]Mo Jiaqi. Solution of travelling wave for nonlinear disturbed long-wave system[J]. Commun Theor Phys,2011,55(2):387-390.
[20]Mo Jiaqi,Lin Yihua,Lin Wantao,et al. Perturbed solving method for interdecadal sea-air oscillator model[J]. Chin Geographical Sci,2012,22(1),42-47.
[21]Mo Jiaqi. Solution of travelling wave for nonlinear disturbed long-wave system[J]. Commun Theor Phys,2011,55(3):387-390.
[22]Mo Jiaqi,Lin Wantao. Generalized variation iteration solution of an atmosphere-ocean oscillator model for global climate[J]. J Sys Sci Complexity,2011,24(2):271-276.
[23]Chen Huaijun,Shi Lanfang,Mo Jiaqi. The generalized interior shock layer solution of nonlinear singularly perturbed equation[J]. J Univ Sci Tech China,2015,15(8):639-643.
[24]Xu Jianzhong,Zhou Zongfu. Existence and uniqueness of anti-periodic solutions for a kind of nonlinear nth-order differential equation with multiple deviating arguments[J]. Ann Diff Eqn,2012,28(1):105-114.
[25]Xu Jianzhong,Zhou Zongfu. Anti-periodic solutions for a kind of nonlinear nth-order differential equation with multiple deviating arguments[J]. J Chongqing Technology and Business Univ,2010,6:545-550.
[26]徐建中,周宗福. 一类具有多个变参数的中立型泛函微分方程的反周期解的存在性[J]. 合肥学院学报,2011,21(4):7-11,36.
Xu Jianzhong,Zhou Zongfu. The existence of anti-periodic solutions for a p-Laplacian neutral functional differential equation with multiple variable parameters[J]. J Hefei Univ,2011,21(4):7-11,36.
[27]徐建中,周宗福. 一类四阶具有多个偏差变元p-Laplacian中立型微分方程周期解的存在性[J]. 重庆工商大学学报,2012,29(11):9-16.
Xu Jianzhong,Zhou Zongfu. The existence of periodic solutions for a class of fourth-order p-Laplacian neutral functional differential equation with multiple deviating arguments[J]. J Chongqing Technology and Business Univ,2012,29(11):9-16.
[28]徐建中,周宗福. 一类具有多个偏差变元高阶微分方程反周期解的存在唯一性[J]. 重庆工商大学学报,2017,34(2):1-5.
Xu Jianzhong,Zhou Zongfu. Existence and uniqueness of anti-periodic solutions for a class of high-order differential equation with multiple deviating arguments[J]. J Chongqing Technology and Business Univ,2017,34(2):1-5.
[29]He Jihua,Wu G C,Austin F. The variational iteration method which should be followed[J]. Nonlinear Sci Lett A,2010,1(1):1-30.
[30]何吉欢. 工程和科学计算中的近似非线性分析方法[M]. 郑州:河南科学技术出版社,2002.
[31]He Jihua,Wu Xianhua. Construction of solitary solution and compacton-like solution by variational iteration method[J]. Chaos Solitions & Fractals,2006,29(1):108-113.

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Last Update: 2019-06-30