Optimal control strategies for reducing the number of active infected individuals with tuberculosis

SIAM Conference on Control and Its Applications 2013

Volumn , Issue , 2013, Pages 44-50

  Rodrigues, Paula ^a   Silva, Cristiana J ^b   Torres, Delfim F M ^b  

^a UNIVERSIDADE NOVA DE LISBOA   (Portugal)

^b UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL ENGINEERING;

OPTIMAL CONTROL PROBLEM; OPTIMAL CONTROL SOLUTION; OPTIMAL CONTROL STRATEGY; POST-EXPOSURE; TRANSMISSION INTENSITY;

OPTIMAL CONTROL SYSTEMS;

EID: 84919351821     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973273.7     Document Type: Conference Paper

References (20)

1. S. Blower, P. Small and P. Hopewell, Control strategies for tuberculosis epidemics: New models for old problems, Science, 273 (1996), pp. 497-500.
2. C. Castillo-Chavez and Z. Feng, Mathematical models for the disease dynamics of tuberculosis, in "Advances in Mathematical Population Dynamics-Molecules, Cells and Man" (eds. Mary Ann Horn, G. Simonett and G. Webb), Vanderbilt University Press, 1998, pp. 117-128.
3. L. Cesari, Optimization - Theory and Applications. Problems with Ordinary Differential Equations, Applications of Mathematics 17, Springer, New York, 1983.
4. T. Cohen and M. Murray, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness, Nat. Med. 10(10) (2004), pp. 1117-1121.
5. C. Dye, G. P. Garnett, K. Sleeman and B. G. Williams, Prospects for worldwide tuberculosis control under the who dots strategy. Directly observed short-course therapy, Lancet, 352 (9144) (1998), pp. 1886-1891.
6. W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer Verlag, New York, 1975.
7. M. Gomes, A. Franco, M. Gomes and G. Medley, The reinfection threshold promotes variability in tuberculosis epidemiology and vaccine efficacy, Proc. R. Soc. B, 271 (1539) (2004), pp. 617-623.
8. 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, J. Theoret. Biol. 248 (2007), no. 4, pp. 608-617.
9. M. G. M. Gomes, L. J. White and G. F. Medley, Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectives, J. Theoret. Biol. 228 (2004), no. 4, pp. 539-549.
10. E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model, Discrete Contin. Dyn. Syst. Ser. B 2 (2002), no. 4, pp. 473-482.
11. T. K. Kar and S. Jana, A theoretical study on mathematical modelling of an infectious disease with application of optimal control, Biosystems. 111 (2013), no. 1, pp. 37-50.
12. L. Pontryagin, V. Boltyanskii, R. Gramkrelidze and E. Mischenko, The Mathematical Theory of Optimal Processes, Wiley Interscience, 1962.
13. P. Rodrigues, C. Rebelo and M. G. M. Gomes, Drug resistance in tuberculosis: A reinfection model, Theor. Popul. Biol. 71 (2007), pp. 196-212.
14. C. J. Silva and D. F. M. Torres, Optimal control strategies for tuberculosis treatment: a case study in Angola, Numer. Algebra Control Optim. 2 (2012), no. 3, pp. 601-617.
15. S. Verver, R. M. Warren, N. Beyers, M. Richardson, G. D. van der Spuy, M. W. Borgdorff, D. A. Enarson, M. A. Behr and P. D. van Helden, Rate of reinfection tuberculosis after successful treatment is higher than rate of new tuberculosis, Am. J. Respir. Crit. Care Med. 171 (2005), pp. 1430-1435.
16. E. Vynnycky and P. E. Fine, The natural history of tuberculosis: the implications of age-dependent risks of disease and the role of reinfection, Epidemiol. Infect. 119(2) (1997), pp. 183-201.
17. WHO, Global Tuberculosis Control, WHO Report, Geneva, 2012.
18. https://projects.coin-or.org/Ipopt
19. http://www.ampl.com
20. http://tomdyn.com