Optimal control of tuberculosis with exogenous reinfection

Applied Mathematical Sciences

Volumn 3, Issue 5, 2009, Pages 231-240

  Hattaf, K ^a   Rachik, M ^a   Saadi, S ^a   Tabit, Y ^a   Yousfi, N ^a  

^a FACULTÉ DES SCIENCES BEN M SIK   (Morocco)

Author keywords

Exogenous reinfection; Optimal control; TB model with exogenous reinfection; Tuberculosis

Indexed keywords

EID: 65549154257     PISSN: None     EISSN: 1312885X     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. B. R. Bloom, Tuberculosis: Pathogenesis, Protection, and Control, ASM Press, Washington, D.C., 1994.
2. C. Castillo-Chavez and Z. Feng, To treat or not to treat: the case of tuberculosis, J. Mathematical Biology, 35 (1997), 629659.
3. Z. Feng, C. Castillo-Chavez, A.F. Capurro, A model for tuberculosis with exogenous reinfection, Theor. Pop. Biol.57, (2000), 235.
4. W. H. Fleming, R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer Verlag, New York, 1975.
5. A. B. Gumel, K. C. Patidar, and R. J. Spiteri, editors, Asymptotically Consistent Non-standard Finite-Difference Methods for Solving Mathematical Models Arising in Population Biology, R. E. Mickens and Worl Scientific, Singapore, 2005.
6. A. B. Gumel, P. N. Shivakumar, and B.M. Sahai, A mathematical model for the dynamics of HIV-1 during the typical course of infection, Third world congress of nonlinear analysts, (2001), 47:20732083.
7. E.Jung, S. Lenhart, Z. Feng, Optimal control of treatments in a two-strain tuberculosis model, Discrete and Continuous Dynamical Systems-Series B, (2002), 2(4): 473482.
8. J. Karrakchou, M. Rachik, and S. Gourari, Optimal control and Infectiology: Application to an HIV/AIDS Model, Applied Mathematics and Computation, (2006), 177:807818.
9. B. Miller, Preventive therapy for tuberculosis, Med. Clin. North Am. 77, (1993), 1263-1275.
10. P. G. Smith, A. R. Moss, Epidemiology of tuberculosis, in "Tuberculosis: Pathogenesis, Protection, and Control", B. R. Bloom, Eds., ASM Press, Washington, 1994.
11. K. Styblo, Epidemiology of Tuberculosis, VEB Gustav Fischer Verlag Jena, The Hague, 1991.
12. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, New York, 1962.