Identification and Parameter Estimation for Classical SIR Model

HE Yan-hui; TANG San-yi

doi:10.3879/j.issn.1000-0887.2013.03.005

Volume 34 Issue 3

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Article Navigation > Applied Mathematics and Mechanics > 2013 > 34(3): 252-258

HE Yan-hui, TANG San-yi. Identification and Parameter Estimation for Classical SIR Model[J]. Applied Mathematics and Mechanics, 2013, 34(3): 252-258. doi: 10.3879/j.issn.1000-0887.2013.03.005

Citation:

HE Yan-hui, TANG San-yi. Identification and Parameter Estimation for Classical SIR Model[J]. Applied Mathematics and Mechanics, 2013, 34(3): 252-258. doi: 10.3879/j.issn.1000-0887.2013.03.005

Citation:

HE Yan-hui, TANG San-yi. Identification and Parameter Estimation for Classical SIR Model[J]. Applied Mathematics and Mechanics, 2013, 34(3): 252-258. doi: 10.3879/j.issn.1000-0887.2013.03.005

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Identification and Parameter Estimation for Classical SIR Model

doi: 10.3879/j.issn.1000-0887.2013.03.005

School of Mathematics and Information Science, Shaanxi Normal University,Xi’an 710062, P.R.China

Received Date: 2013-01-15
Rev Recd Date: 2012-12-19
Publish Date: 2013-03-15

Abstract

Abstract

Whether a model can be identified is a basic characteristic of the model before studying parameter estimation. Until recently, the classical susceptibleinfectiousrecovered (SIR) model is still one of the most commonly used models. In present work the algebraic identifiability of the SIR model by using highorder derivative method (HODM) and multiple time points method (MTPM) was studied. The results indicatet that the SIR model can be identified if only the infectious was reported, and MTPM is much beter than HODM. Using the data of the flu, the least square method was adopted to estimate the parameters of the SIR model. The result further confirmed that the SIR model was identifiable. The methods developed here could be applied to investigate other type models and left those for future studies.
- identifiability,
- HODM,
- MTPM,
- identification function,
- parameter estimation

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References(6)

References

[1]	Conte G, Moog C H, Perdon A M. Nonlinear Control Systems: an Algebraic Setting [M].London: Springer, 1999.
[2]	Xia X, Moog C H.Identifiability of nonlinear systems with application to HIV/AIDS models[J].IEEE Transactions on Automatic Control , 2003, 48(2): 330-336.
[3]	Jeffrey A M, Xia X. Identifiability of HIV/AIDS Models(Chaptern) .In: Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections With Intervention [M].Singapore: World Scientific Publishing, 2005.
[4]	Wu H, Zhu H, Miao H, Perelson A S.Parameter identifiability and estimation of HIV/AIDS dynamic models[J]. Bulletin of Mathematical Biology , 2008, 70(3): 785-799.
[5]	肖燕妮, 周义仓, 唐三一.生物数学原理[M].西安: 西安交通大学出版社, 2012.（XIAO Yan-ni, ZHOU Yi-cang, TANG San-yi. The Principle of Biomathematics [M].Xi’an: Xi’an Jiaotong University Press, 2012（in Chinese））
[6]	Roger A H, Charles R J.矩阵分析[M].杨奇译.机械工业出版社, 1985.（Roger A H, Charles R J. Matrix Analysis [M].YANG Qi, Transl. Mechanical Industry Press, 1985.（in Chinese））

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