Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 104764, 11 pages
http://dx.doi.org/10.1155/2014/104764
Research Article

Robust Sliding Control of SEIR Epidemic Models

1Departament de Telecomunicació i Enginyeria de Sistemes, School of Engineering, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
2Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, P.O.Box 644, 48080 Bilbao, Spain

Received 12 November 2013; Revised 14 January 2014; Accepted 15 January 2014; Published 13 March 2014

Academic Editor: Xinzhu Meng

Copyright © 2014 Asier Ibeas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals, Princeton University Press, Princeton, NJ, USA, 2008. View at MathSciNet
  2. S. Zhang and Y. Zhou, “Dynamics and application of an epidemiological model for hepatitis C,” Mathematical and Computer Modelling, vol. 56, no. 1-2, pp. 36–42, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. D. O. Gerardi and L. H. A. Monteiro, “System identification and prediction of dengue fever incidence in Rio de Janeiro,” Mathematical Problems in Engineering, vol. 2011, Article ID 720304, 13 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. F. A. C. C. Chalub and M. O. Souza, “The SIR epidemic model from a PDE point of view,” Mathematical and Computer Modelling, vol. 53, no. 7-8, pp. 1568–1574, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. X. Zhou and J. Cui, “Stability and Hopf bifurcation analysis of an eco-epidemiological model with delay,” Journal of the Franklin Institute, vol. 347, no. 9, pp. 1654–1680, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Q. Gan, R. Xu, Y. Li, and R. Hu, “Travelling waves in an infectious disease model with a fixed latent period and a spatio-temporal delay,” Mathematical and Computer Modelling, vol. 53, no. 5-6, pp. 814–823, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. N. Yi, Q. Zhang, K. Mao, D. Yang, and Q. Li, “Analysis and control of an SEIR epidemic system with nonlinear transmission rate,” Mathematical and Computer Modelling, vol. 50, no. 9-10, pp. 1498–1513, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. X. Zhou and J. Cui, “Analysis of stability and bifurcation for an SEIR epidemic model with saturated recovery rate,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, pp. 4438–4450, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. de la Sen, R. P. Agarwal, A. Ibeas, and S. Alonso-Quesada, “On the existence of equilibrium points, boundedness, oscillating behavior and positivity of a SVEIRS epidemic model under constant and impulsive vaccination,” Advances in Difference Equations, vol. 2011, Article ID 748608, 32 pages, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. B. Mukhopadhyay and R. Bhattacharyya, “Existence of epidemic waves in a disease transmission model with two-habitat population,” International Journal of Systems Science, vol. 38, no. 9, pp. 699–707, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Li, Y. Xiao, F. Zhang, and Y. Yang, “An algebraic approach to proving the global stability of a class of epidemic models,” Nonlinear Analysis: Real World Applications, vol. 13, no. 5, pp. 2006–2016, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Bowong and J. J. Tewa, “Global analysis of a dynamical model for transmission of tuberculosis with a general contact rate,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 11, pp. 3621–3631, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. H. Chen and J. Sun, “Global stability of delay multigroup epidemic models with group mixing and nonlinear incidence rates,” Applied Mathematics and Computation, vol. 218, no. 8, pp. 4391–4400, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. P. Tian and J. Wang, “Global stability for cholera epidemic models,” Mathematical Biosciences, vol. 232, no. 1, pp. 31–41, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. H. Shu, D. Fan, and J. Wei, “Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission,” Nonlinear Analysis: Real World Applications, vol. 13, no. 4, pp. 1581–1592, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. S.-Z. Huang, “A new SEIR epidemic model with applications to the theory of eradication and control of diseases, and to the calculation of R0,” Mathematical Biosciences, vol. 215, no. 1, pp. 84–104, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. de la Sen, A. Ibeas, and S. Alonso-Quesada, “On vaccination controls for the SEIR epidemic model,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 6, pp. 2637–2658, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. M. de la Sen, A. Ibeas, and S. Alonso-Quesada, “Feedback linearization-based vaccination control strategies for true-mass action type SEIR epidemic models,” Nonlinear Analysis: Modelling and Control, vol. 16, no. 3, pp. 283–314, 2011. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. S. Alonso-Quesada, M. de la Sen, R. P. Agarwal, and A. Ibeas, “Anobserver-based vaccination control law for an SEIR epidemic modelbased on feedback linearization techniques for nonlinear systems,” Advances in Difference Equations, vol. 2012, p. 161, 2012. View at Publisher · View at Google Scholar
  20. S. Gao, L. Chen, and Z. Teng, “Pulse vaccination of an SEIR epidemic model with time delay,” Nonlinear Analysis: Real World Applications, vol. 9, no. 2, pp. 599–607, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. S. Gao, Z. Teng, and D. Xie, “The effects of pulse vaccination on SEIR model with two time delays,” Applied Mathematics and Computation, vol. 201, no. 1-2, pp. 282–292, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. C.-Y. Chen and G. T.-C. Chiu, “H∞ robust controller design of media advance systems with time domain specifications,” International Journal of Innovative Computing, Information and Control, vol. 4, no. 4, pp. 813–828, 2008. View at Google Scholar · View at Scopus
  23. S. Tong, W. Wang, and L. Qu, “Decentralized robust control for uncertain T-S fuzzy large-scale systems with time-delay,” International Journal of Innovative Computing, Information and Control, vol. 3, no. 3, pp. 657–672, 2007. View at Google Scholar · View at Scopus
  24. M. Wang, X. Liu, and P. Shi, “Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 41, no. 6, pp. 1681–1692, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. A. Ibeas and M. de la Sen, “Robust sliding control of robotic manipulators based on a heuristic modification of the sliding gain,” Journal of Intelligent and Robotic Systems, vol. 48, no. 4, pp. 485–511, 2007. View at Publisher · View at Google Scholar · View at Scopus
  26. C. Yang, Z. Yang, X. Huang, S. Li, and Q. Zhang, “Modeling and robust trajectory tracking control for a novel six-rotor unmanned aerial vehicle,” Mathematical Problems in Engineering, vol. 2013, Article ID 673525, 13 pages, 2013. View at Google Scholar · View at MathSciNet
  27. Z. Xiao-Yu, Z. Yu-Xin, X. De-Xin, and H. Kun-Peng, “Sliding mode control for mass moment aerospace vehicles using dynamic inversion approach,” Mathematical Problems in Engineering, vol. 2013, Article ID 284869, 11 pages, 2013. View at Publisher · View at Google Scholar
  28. Y.-C. Chung, B.-J. Wen, and Y.-C. Lin, “Optimal fuzzy sliding-mode control for bio-microfluidic manipulation,” Control Engineering Practice, vol. 15, no. 9, pp. 1093–1105, 2007. View at Publisher · View at Google Scholar · View at Scopus
  29. M. K. Khan and S. K. Spurgeon, “Robust MIMO water level control in interconnected twin-tanks using second order sliding mode control,” Control Engineering Practice, vol. 14, no. 4, pp. 375–386, 2006. View at Publisher · View at Google Scholar · View at Scopus
  30. H. Lee and V. I. Utkin, “Chattering suppression methods in sliding mode control systems,” Annual Reviews in Control, vol. 31, no. 2, pp. 179–188, 2007. View at Publisher · View at Google Scholar · View at Scopus
  31. O. Barambones and P. Alkorta, “A robust vector control for induction motor drives with an adaptive sliding-mode control law,” Journal of the Franklin Institute, vol. 348, no. 2, pp. 300–314, 2011. View at Publisher · View at Google Scholar · View at Scopus
  32. O. Barambones, J. M. Gonzalez de Durana, and M. de la Sen, “Robust speed control for a variable speed wind turbine,” International Journal of Innovative Computing, Information and Control, vol. 8, no. 11, pp. 7627–7640, 2012. View at Google Scholar
  33. A. Ibeas, M. de la Sen, and S. Alonso-Quesada, “Sliding mode robust control of SEIR epidemic models,” in Proceedings of the 21st Iranian Conference on Electrical Engineering, Mashhad, Iran, May 2013.
  34. J. J. Slotine, Applied Nonlinear Control, Prentice, 1994.