Optimal control strategies for tuberculosis treatment: A case study in Angola

Numerical Algebra, Control and Optimization

Volumn 2, Issue 3, 2012, Pages 601-617

  Silva, Cristiana J ^a   Torres, Delfim F M ^a  

^a UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Angola; Epidemiology; Optimal control; Treatment strategies; Tuberculosis

Indexed keywords

EID: 84892398225     PISSN: 21553289     EISSN: 21553297     Source Type: Journal    
DOI: 10.3934/naco.2012.2.601     Document Type: Article

References (32)

1. L. Cesari, "Optimization-Theory and Applications. Problems with Ordinary Differential Eèuations, " Applications of Mathematics 17, Springer-Verlag, New York, 1983.
2. A. D'Onofrio, U. Ledzewicz, H. Maurer and H. Schättler, On optimal delivery of combination therapy for tumors, Math. Biosci., 222 (2009), 13-26.
3. C. Dye, S. Scheele, P. Dolin, V. Pathania and M. C. Raviglione, Global burden of tuberculosis. Estimated incidence, prevalence, and mortality by country, Journal of the American Medical Association, 282 (1999), 677-686.
4. W. H. Fleming and R. W. Rishel, "Deterministic and Stochastic Optimal Control, " Applications of Mathematics, No. 1, Springer-Verlag, Berlin-New York, 1975.
5. M. G. M. Gomes, P. Rodrigues, F. M. Hilker, N. B. Mantilla-Beniers, M. Muehlen, A. C. Paulo and G. F. Medley, Implications of partial immunity on the prospects for tuberculosis control by post-exposure interventions, Journal of Theoretical Biology, 248 (2007), 608-617.
6. L. S. Jennings, M. E. Fisher, K. L. Teo and C. J. Goh, "MISER3 Optimal Control Software: Theory and User Manual, " Version 3.3, Department of Mathematics, The University of Western Australia, Nedlands, Australia, 2004.
7. E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model, Discrete and Continuous Dynamical Systems-Series B, 2 (2002), 473-482.
8. M. E. Kruk, N. R. Schwalbe and C. A. Aguiar, Timing of default from tuberculosis treatment: a systematic review, Tropical Medicine and International Health, 13 (2008), 703-712.
9. U. Ledzewicz, J. Marriott, H. Maurer and H. Schättler, Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment, Math. Med. Biol., 27 (2010), 157-179.
10. U. Ledzewicz, H. Maurer and H. Schättler, Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy, Math. Biosci. Eng., 8 (2011), 307-323.
11. S. Lenhart and J. T. Workman, "Optimal Control Applied to Biological Models, " Chapman & Hall/CRC, Boca Raton, FL, 2007.
12. R. C. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints, Automatica J. IFAC, 44 (2008), 2923-2929.
13. L. Pontryagin, V. Boltyanskii, R. Gramkrelidze and E. Mischenko, "The Mathematical Theory of Optimal Processes, " Wiley Interscience, 1962.
14. H. S. Rodrigues, M. T. T. Monteiro and D. F. M. Torres, Dynamics of dengue epidemics when using optimal control, Math. Comput. Modelling, 52 (2010), 1667-1673.
15. H. S. Rodrigues, M. T. T. Monteiro, D. F. M. Torres and A. Zinober, Dengue disease, basic reproduction number and control, Int. J. Comput. Math., 89 (2012), 334-346.
16. P. M. Small and P. I. Fujiwara, Management of tuberculosis in the United States, N. Engl. J. Med., 345 (2001), 189-200.
17. K. Styblo, State of art: epidemiology of tuberculosis, Bull. Int. Union Tuberc., 53 (1978), 141-152.
18. K. Styblo, "Selected Papers, Epidemiology of Tuberculosis, " Royal Netherlands Tuberculosis Association, 24, 1991.
19. K. L. Teo, C. J. Goh and K. H. Wong, "A Unified Computational Approach to Optimal Control Problems, " Pitman Monographs and Surveys in Pure and Applied Mathematics, 55, Longman Sci. Tech., Harlow, 1991.
20. WHO, Treatment of tuberculosis guidelines, Fourth edition, WHO, Geneva, 2010. Available from: http://www.who.int/tb/publications/tb_treatmentguidelines/en/index.html.
21. WHO, Global Tuberculosis Control, WHO Report 2011, Geneva, 2011. Available from: http://www.who.int/tb/publications/global_report/en/index.html.
22. http://allafrica.com/stories/201103240476.html.
23. http://apps.who.int/ghodata/?theme=country.
24. http://www.avert.org/tuberculosis.htm.
25. http://www.minsa.gov.ao/VerNoticia.aspx?id=10499.
26. https://projects.coin-or.org/Ipopt.
27. http://www.ampl.com.
28. http://tomdyn.com.
29. http://www.minsa.gov.ao/VerNoticia.aspx?id=8797.
30. http://www.tradingeconomics.com/angola/tuberculosis-case-detection-rate-all-forms-wb-data.html.
31. http://www.usaid.gov/our_work/global_health/id/tuberculosis/countries/africa/angola_profile.html.
32. http://www.who.int/en/.