全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

具一般非线性接触率、隔离和染病年龄结构的 SIQS模型非负解的存在惟一性

, PP. 43-48

Keywords: 隔离,非线性接触率,染病年龄,SIQS传染病模型,非负解

Full-Text   Cite this paper   Add to My Lib

Abstract:

染病年龄的引入使传染率依赖于染病年龄,这样所建立的模型更适合染病期较长的疾病,如AIDS等.而且从形式上讲,模型是常微分方程和偏微分方程相结合的微分方程模型.对这类模型非负解存在性及惟一性研究具有重要的理论意义,正被广大学者关注.首先,将SIQS传染病模型引入了一般非线性接触率及染病年龄结构建立了一类新的SIQS传染病模型,继而综合运用Bellman-Grownall引理、不动点定理讨论模型非负解的存在性及惟一性,最后由延拓方法将解延拓到正半实数轴.

References

[1]  Thieme H R, Castillo-Chavez C. How may infection-age-dependent infectivity affect the dynamics of HIV/AIDS?[J]. SIAM J Appl Math,1993,53(5):1447-1479.
[2]  Kim M Y, Milner F A. A mathematical model of epidemics with screening and variable infectivity[J]. Math Comput Modelling,1995,21(7):29-42.
[3]  Kim M Y. Existence of steady state solutions to an epidemic model with screening and their asymptotic stability[J]. Appl Math Comput,1996,74(1):37-58.
[4]  Kribs-Zaleta C M, Martcheva M. Vaccination strategies and backward bifurcation in an age-since-infection structured model[J]. Math Biosci,2002,177/178:317-332.
[5]  Inaba H, Sekine H. A mathematical model for Chagas disease with infection-age-dependent infectivity[J]. Math Biosci,2004,190(1):39-69.
[6]  Li J, Zhou Y C, Ma Z, et al. Epidemiological models for mutating pathogens[J]. SIAM J Appl Math,2004,65(1):1-23.
[7]  Sattenspiel L, Herring D A. Simulating the effect of guarantine on the spread of the 1918-19 flu in central Ganada[J]. Bull Math Biol,2003,65(1):1-26.
[8]  Hethcote H W, Ma Z, Liao S B. Effects of quarantine in six endemic models for infectious disease[J]. Math Biosci,2002,180(1/2):141-160.
[9]  Zhang Z H, Peng J P. A SIRS epidemic model with infection-age dependence[J]. J Math Anal Appl,2007,331(2):1396-1414.
[10]  徐文雄,张仲华. 年龄结构SIR流行病传播数学模型渐近分析[J]. 西安交通大学学报:自然科学版,2003,37(10):1086-1089.
[11]  He Z R, Wang H T. Control problems of an age-dependent pradator-prey system[J]. Applied Math J Chinese Uinversity,2009,B24(3):253-262.
[12]  Busenberg S, Iannelli M. Separable models in age-dependent population dynamics[J]. J Mathematical Biology,1985,22(2):145-173.
[13]  Chiu A Y, Zhai P, Dal Canto M C, et al. Age-dependence penetrance of disease in a transgenic mouse model of familial amyotrophic lateral sclerosis[J]. Molecular and Cellular Neuroscience,1995,6(4):349-362.
[14]  Pollock K H. Capture-recapture model allowing for age-dependent survival and capture rates[J]. Biometrics,1981,37(3):521-529.
[15]  Allen L J S, Thrasher D B. The effects of vaccination in an age-dependent model for varicella and herpes zoster[J]. IEEE Transactions on Automatic Control,1998,43(6):779-789.
[16]  Greenhalgh D. Threshold and stability results for an epidemic model with an age-structured meeting rate[J]. Mathematical Medicine and Biology,1985,5(2):81-100.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133