Hybrid Taguchi-differential evolution algorithm for parameter estimation of differential equation models with application to HIV dynamics

Mathematical Problems in Engineering

Volumn 2011, Issue , 2011, Pages

  Ho, Wen Hsien ^a   Chan, Agnes Lai Fong ^b  

^a KAOHSIUNG MEDICAL UNIVERSITY   (Taiwan)

^b CHI MEI MEDICAL CENTER   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATION MODEL; DIFFERENTIAL EVOLUTION; DIFFERENTIAL EVOLUTION ALGORITHMS; DYNAMICAL MODEL; HIV DYNAMICS; HUMAN IMMUNODEFICIENCY VIRUS; ILLUSTRATIVE EXAMPLES; OPTIMAL SOLUTIONS; ROBUST OPTIMAL SOLUTIONS; TAGUCHI;

DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); DISEASES; EVOLUTIONARY ALGORITHMS; METAL ANALYSIS; NUMERICAL METHODS; OPTIMAL SYSTEMS; OPTIMIZATION; VIRUSES;

PARAMETER ESTIMATION;

EID: 78650746523     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2011/514756     Document Type: Article

References (41)

1. Perelson A. S., Nelson P. W., Mathematical analysis of HIV-1 dynamics in vivo SIAM Review 1999 41 1 3 44
2. Bonhoeffer S., Rembiszewski M., Ortiz G. M., Nixon D. F., Risks and benefits of structured antiretroviral drug therapy interruptions in HIV-1 infection AIDS 2000 14 15 2313 2322
3. Wodarz D., Helper-dependent vs. helper-independent CTL responses in HIV infection: implications for drug therapy and resistance Journal of Theoretical Biology 2001 213 3 447 459
4. Wodarz D., Nowak M. A., Mathematical models of HIV pathogenesis and treatment BioEssays 2002 24 12 1178 1187
5. Culshaw R. V., Ruan S., Webb G., A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay Journal of Mathematical Biology 2003 46 5 425 444
6. Katri P., Ruan S., Dynamics of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells Comptes Rendus Biologies 2004 327 11 1009 1016
7. Adams B. M., Banks H. T., Davidian M., Kwon H.-D., Tran H. T., Wynne S. N., Rosenberg E. S., HIV dynamics: modeling, data analysis, and optimal treatment protocols Journal of Computational and Applied Mathematics 2005 184 1 10 49
8. Murase A., Sasaki T., Kajiwara T., Stability analysis of pathogen-immune interaction dynamics Journal of Mathematical Biology 2005 51 3 247 267
9. Karrakchou J., Rachik M., Gourari S., Optimal control and infectiology: application to an HIV/AIDS model Applied Mathematics and Computation 2006 177 2 807 818
10. Dumrongpokaphan T., Lenbury Y., Ouncharoen R., Xu Y., An intracellular delay-differential equation model of the HIV infection and immune control Mathematical Modelling of Natural Phenomena 2007 2 1 84 112
11. Zhu H., Zou X., Impact of delays in cell infection and virus production on HIV-1 dynamics Mathematical Medicine and Biology 2008 25 2 99 112
12. Burg D., Rong L., Neumann A. U., Dahari H., Mathematical modeling of viral kinetics under immune control during primary HIV-1 infection Journal of Theoretical Biology 2009 259 4 751 759
13. Radisavljevic-Gajic V., Optimal control of HIV-virus dynamics Annals of Biomedical Engineering 2009 37 6 1251 1261
14. Rao A., Thomas K., Sudhakar K., Maini P. K., HIV/AIDS epidemic in India and predicting the impact of the national response: mathematical modeling and analysis Mathematical Biosciences and Engineering 2009 6 4 779 813
15. Wang X., Tao Y., Song X., A delayed HIV-1 infection model with Beddington-DeAngelis functional response Nonlinear Dynamics 2010 62 67 72
16. Wu H., Ding A. A., De Gruttola V., Estimation of HIV dynamic parameters Statistics in Medicine 1998 17 21 2463 2485
17. Putter H., Heisterkamp S. H., Lange J. M. A., De Wolf F., A Bayesian approach to parameter estimation in HIV dynamical models Statistics in Medicine 2002 21 15 2199 2214
18. Xia X., Estimation of HIV/AIDS parameters Automatica 2003 39 11 1983 1988
19. Xia X., Moog C. H., Identifiability of nonlinear systems with application to HIV/AIDS models IEEE Transactions on Automatic Control 2003 48 2 330 336
20. Ciupe M. S., Bivort B. L., Bortz D. M., Nelson P. W., Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models Mathematical Biosciences 2006 200 1 1 27
21. Huang Y., Liu D., Wu H., Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system Biometrics 2006 62 2 413 423
22. Manseur S., Messaoudi N., Cherruault Y., Parameter identification of an HIV model by the combined Adomian/Alienor method Kybernetes 2006 35 10 1725 1734
23. Wu H., Zhu H., Miao H., Perelson A. S., Parameter identifiability and estimation of HIV/AIDS dynamic models Bulletin of Mathematical Biology 2008 70 3 785 799
24. Miao H., Dykes C., Demeter L. M., Wu H., Differential equation modeling of HIV viral fitness experiments: model identification, model selection, and multimodel inference Biometrics 2009 65 1 292 300
25. Liang H., Miao H., Wu H., Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model Annals of Applied Statistics 2010 4 460 483
26. Storn R., Price K., Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces 1995 TR-95-012 Berkeley, Calif, USA International Computer Science Institute
27. Liu J., Lampinen J., A fuzzy adaptive differential evolution algorithm Soft Computing 2005 9 6 448 462
28. Angira R., Babu B. V., Optimization of process synthesis and design problems: a modified differential evolution approach Chemical Engineering Science 2006 61 14 4707 4721
29. Kim H.-K., Chong J.-K., Park K.-Y., Lowther D. A., Differential evolution strategy for constrained global optimization and application to practical engineering problems IEEE Transactions on Magnetics 2007 43 4 1565 1568
30. Onwubolu G. C., Design of hybrid differential evolution and group method of data handling networks for modeling and prediction Information Sciences 2008 178 18 3616 3634
31. Takahama T., Sakai S., Hara A., Iwane N., Predicting stock price using neural networks optimized by differential evolution with degeneration International Journal of Innovative Computing, Information and Control 2009 5 12 5021 5031
32. Ho W.-H., Chou J.-H., Guo C.-Y., Parameter identification of chaotic systems using improved differential evolution algorithm Nonlinear Dynamics 2010 61 29 41
33. Noktehdan A., Karimi B., Husseinzadeh Kashan A., A differential evolution algorithm for the manufacturing cell formation problem using group based operators Expert Systems with Applications 2010 37 7 4822 4829
34. Tsai J.-T., Ho W.-H., Chou J.-H., Guo C.-Y., Optimal approximation of linear systems using Taguchi-sliding-based differential evolution algorithm. Applied Soft Computing Journal. In press
35. Storn R., System design by constraint adaptation and differential evolution IEEE Transactions on Evolutionary Computation 1999 3 1 22 34
36. Price K. V., Storn R. M., Lampinen J. A., Differential Evolution: A Practical Approach to Global Optimization 2005 Berlin, Germany Springer xx+538 Natural Computing Series
37. Nowak M. A., Bangham C. R. M., Population dynamics of immune responses to persistent viruses Science 1996 272 5258 74 79
38. Taguchi G., Chowdhury S., Taguchi S., Robust Engineering 2000 New York, NY, USA McGraw-Hill
39. Wu Y., Taguchi Methods for Robust Design 2000 New York, NY, USA The American Society of Mechanical Engineers
40. Tsai J.-T., Liu T.-K., Chou J.-H., Hybrid Taguchi-genetic algorithm for global numerical optimization IEEE Transactions on Evolutionary Computation 2004 8 4 365 377
41. Tsai J.-T., Chou J.-H., Liu T.-K., Tuning the structure and parameters of a neural network by using hybrid Taguchi-genetic algorithm IEEE Transactions on Neural Networks 2006 17 1 69 80