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Abstract and Applied Analysis
Volume 2014, Article ID 954069, 18 pages
http://dx.doi.org/10.1155/2014/954069
Research Article

Optimal Control Strategies in an Alcoholism Model

1College of Electrical and Information Engineering, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
2Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China
3School of Electrical and Information Engineering, Anhui Industrial University, Maanshan, Anhui 243032, China

Received 10 December 2013; Accepted 9 January 2014; Published 2 March 2014

Academic Editor: Weiming Wang

Copyright © 2014 Xun-Yang Wang 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. R. Room, T. Babor, and J. Rehm, “Alcohol and public health,” The Lancet, vol. 365, no. 9458, pp. 519–530, 2005. View at Publisher · View at Google Scholar · View at Scopus
  2. J. B. Saunders, O. G. Aasland, A. Amundsen, and M. Grant, “Alcohol consumption and related problems among primary health care patients: WHO collaborative project on early detection of persons with harmful alcohol consumption I,” Addiction, vol. 88, no. 3, pp. 349–362, 1993. View at Google Scholar · View at Scopus
  3. L. D. Johnston, P. M. OMalley, and J. G. Bachman, National Survey Results on Drug Use From the Monitoring the Future Study, 1975–1992, National Institute on Drug Abuse, Rockville, Md, USA, 1993.
  4. H. Wechsler, J. E. Lee, M. Kuo, and H. Lee, “College binge drinking in the 1990s: a continuing problem. Results of the Harvard School of Public Health 1999 College Alcohol Study,” Journal of American College Health, vol. 48, no. 5, pp. 199–210, 2000. View at Google Scholar · View at Scopus
  5. P. M. O'Malley and L. D. Johnston, “Epidemiology of alcohol and other drug use among American college students,” Journal of Studies on Alcohol, vol. 63, no. 14, pp. 23–39, 2002. View at Google Scholar · View at Scopus
  6. K. Agarwal-Kozlowski and D. P. Agarwal, “Genetic predisposition to alcoholism,” Therapeutische Umschau, vol. 57, no. 4, pp. 179–184, 2000. View at Google Scholar · View at Scopus
  7. C. Y. Chen, C. L. Storr, and J. C. Anthony, “Early-onset drug use and risk for drug dependence problems,” Addictive Behaviors, vol. 34, no. 3, pp. 319–322, 2009. View at Google Scholar
  8. M. Glavas and J. Weinberg, “Stress, alcohol consumption and the hypothalamic-pituitary adrenal axis,” in Nutrients, Stress and Medical Disorders, pp. 165–183, Humana Press, New York, NY, USA, 2006. View at Google Scholar
  9. L. N. Blum, N. H. Nielsen, J. A. Riggs, and L. B. Bresolin, “Alcoholism and alcohol abuse among women: report of the Council on Scientific Affairs,” Journal of Women's Health, vol. 7, no. 7, pp. 861–871, 1998. View at Google Scholar · View at Scopus
  10. B. Benedict, “Modeling alcoholism as a contagious disease: how “infected” drinking buddies spread problem drinking,” SIAM News, vol. 40, no. 3, 2007. View at Google Scholar
  11. H. Walter, K. Gutierrez, K. Ramskogler, I. Hertling, A. Dvorak, and O. M. Lesch, “Gender-specific differences in alcoholism: Implications for treatment,” Archives of Women's Mental Health, vol. 6, no. 4, pp. 253–258, 2003. View at Publisher · View at Google Scholar · View at Scopus
  12. D. Müller, R. D. Koch, H. von Specht, w. Völker, and E. M. Münch, “Neurophisiologic findings in chronic alcohol abuse,” Psychiatrie, Neurologie, und Medizinische Psychologie, vol. 37, no. 3, pp. 129–132, 1985. View at Google Scholar
  13. G. Testino, “Alcoholic diseases in hepato-gastroenterology: a point of view,” Hepato-Gastroenterology, vol. 55, no. 82-83, pp. 371–377, 2008. View at Google Scholar · View at Scopus
  14. A. Mubayi, P. E. Greenwood, C. Castillo-Chávez, P. J. Gruenewald, and D. M. Gorman, “The impact of relative residence times on the distribution of heavy drinkers in highly distinct environments,” Socio-Economic Planning Sciences, vol. 44, no. 1, pp. 45–56, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. D. Müller, R. D. Koch, H. von Specht, W. Völker, and E. M. Münch, “Neurophysiologic findings in chronic alcohol abuse,” Psychiatrie, Neurologie, Und Medizinische Psychologie, vol. 37, no. 3, pp. 129–132, 1985, (Leipz). View at Google Scholar
  16. G. Mulone and B. Straughan, “Modeling binge drinking,” International Journal of Biomathematics, vol. 5, no. 1, Article ID 1250005, 14 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  17. H. F. Huo and N. N. Song, “Global stability for a binge drinking model with two stages,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 829386, 15 pages, 2012. View at Publisher · View at Google Scholar
  18. S. S. Mushayabasa and C. P. Bhunu, “Modelling the effects of heavy alcohol consumption on the transmission dynamics of gonorrhea,” Nonlinear Dynamics, vol. 66, no. 4, pp. 695–706, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. F. S. Sáncheznchez, X. Wang, C. Castillo-Chvez, D. M. Gorman, and P. J. Gruenewald, “Drinking as an epidemic: a simple mathematical model with recovery and relapse,” in Therapists Guide to Evidence-Based Relapse Prevention, K. Witkiewitz and G. Marlatt, Eds., Academic Press, New York, NY, USA, 2007. View at Google Scholar
  20. H.-F. Huo and C.-C. Zhu, “Influence of relapse in a giving up smoking model,” Abstract and Applied Analysis, vol. 2013, Article ID 525461, 12 pages, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. H. F. Huo and Q. Wang, “The effects of awareness programs by 17 media on the drinking dynamics,” Submitted.
  22. S. Lee, E. Jung, and C. Castillo-Chavez, “Optimal control intervention strategies in low- and high-risk problem drinking populations,” Socio-Economic Planning Sciences, vol. 44, no. 4, pp. 258–265, 2010. View at Publisher · View at Google Scholar · View at Scopus
  23. K. R. Fister, S. Lenhart, and J. S. McNally, “Optimizing chemotherapy in an HIV model,” Electronic Journal of Differential Equations, vol. 1998, no. 32, pp. 1–12, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. S. Lenhart and J. T. Workman, Optimal Control Applied to Biological Models, Chapman & Hall/CRC Mathematical and Computational Biology Series, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2007. View at MathSciNet
  25. X. Yang, L. Chen, and J. Chen, “Permanence and positive periodic solution for the single-species nonautonomous delay diffusive models,” Computers & Mathematics with Applications. An International Journal, vol. 32, no. 4, pp. 109–116, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  26. P. van den Driessche and J. Watmough, “Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,” Mathematical Biosciences, vol. 180, pp. 29–48, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. V. Lakshmikantham, S. Leela, and A. A. Martynyuk, Stability Analysis of Nonlinear Systems, vol. 125, Marcel Dekker, New York, NY, USA, 1989. View at MathSciNet
  28. J. P. LaSalle, The Stability of Dynamical Systems, vol. 25 of Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics, 1976. View at MathSciNet
  29. W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, vol. 1 of Applications of Mathematics, Springer, Berlin, Germany, 1975. View at MathSciNet
  30. D. L. Lukes, Differential Equations: Classical to Controlled, Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1982. View at MathSciNet
  31. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, John Wiley & Sons, New Jersey, NJ, USA, 1962. View at MathSciNet
  32. W. Hackbusch, “A numerical method for solving parabolic equations with opposite orientations,” Computing, vol. 20, no. 3, pp. 229–240, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet