A two strain tuberculosis transmission model with therapy and quarantine

References

• Ackleh , A.S. and Allen , L.J.S. 2004 . Competitive exclusion in SIS and SIR epidemic models with total cross immunity and density‐dependent host mortality . Discrete and Continuous Dynamical Systems Series B , (in press)
   Google Scholar
• Allen , L.J.S. , Langais , M. and Phillips , C.J. 2003 . The dynamics of two viral infections in a single host population with applications to hantavirus . Mathematics Biosciences, , 186 : 191 – 217 .
   PubMed Web of Science ®Google Scholar
• Birkoff , G. and Rota , G.C. 1982 . Ordinary Differential Equations , Ginn .
   Google Scholar
• Blower , S.M. and Gerberding , J.L. 1998 . Understanding, predicting and controlling the emergence of drug‐resistant tuberculosis: a theoretical framework . Journal of Molecular Medicine, , 76 : 624 – 636 .
   PubMedGoogle Scholar
• Blyuss , K.B. and Kyrychko , Y.N. 2005 . On a basic model of a two‐disease epidemic . Applied Mathematics and Computation, , 160 : 177 – 187 .
   Web of Science ®Google Scholar
• Carr , J. 1981 . Applications Centre Manifold theory. , New York : Springer‐Verlag .
   Google Scholar
• Castillo‐Chavez , C. and Feng , Z. 1997 . To treat or not to treat: The case of tuberculosis . Journal of Mathematical Biology, , 35 : 629 – 656 .
   PubMed Web of Science ®Google Scholar
• Castillo‐Chavez , C. and Feng , Z. 1998 . Mathematical models for the disease dynamics of tuberculosis , 629 – 656 . World Scientific Press .
   Google Scholar
• Castillo‐Chavez , C. and Song , B. 2004 . Dynamical models of tuberculosis and their applications . Mathematical Bioscience and Engineering, , 1 (2) : 361 – 404 .
   PubMedGoogle Scholar
• Coleman , D.C. and Slutkin , G. 1984 . Chemoprophylaxis against tuberculosis [Topics in primary care medicine] . West. J. Med., , 40 (1) : 106 – 110 .
   Google Scholar
• Corbet , E.L. , Watt , C.J. and Walker , N. 2003 . The growing burden of tuberculosis: global trends and interactions with the HIV epidemic . Arch. Intern. Med., , 163 : 1009 – 1021 .
   PubMedGoogle Scholar
• Davies , P.D.O. 1999 . Multi‐drug resistant tuberculosis. , Priory Lodge Education Ltd .
   Google Scholar
• van den Driesche , P. and Watmough , J. 2002 . Reproduction numbers and sub‐threshold endemic equilibria for the compartmental models of disease transmission . Mathematics Biosciences, , 180 : 29 – 48 .
   PubMed Web of Science ®Google Scholar
• Dye , C. , Schele , S. , Dolin , P. , Pathania , V. and Raviglione , M. 1998 . Prospects for worldwide tuberculosis control under the WHO DOTS strategy. Directly observed short‐course therapy . The Lancet, , 352 : 1886 – 1891 .
   PubMed Web of Science ®Google Scholar
• Dye , C. and William , B.G. 2000 . Criteria for the control of drug resistant tuberculosis . Proc. Natl. Acad. Sci. USA, , 97 : 8180 – 8185 .
   PubMed Web of Science ®Google Scholar
• Feng , Z. , Castillo‐Chavez , C. and Capurro , A.F. 2000 . A model for tuberculosis with exogenous reinfection . Theor. Pop. Bio., , 57 : 235 – 247 .
   PubMed Web of Science ®Google Scholar
• Frieden , T. , Sterling , T.R. , Munsiff , S.S. , Watt , C.J. and Dye , C. 2003 . Tuberculosis . Lancet, , 362 : 887 – 899 .
   PubMed Web of Science ®Google Scholar
• Martcheva , M. , Ianelli , M. and Xue‐Zhi‐Li . 2007 . Subthreshold coexistence of strains: The impact of vaccination and mutation . Mathematical Bioscience and Engineering, , 4 (2) : 287 – 317 .
   PubMedGoogle Scholar
• May , R. and Nowak , M. 1995 . Coinfection and the evolution of parasite virulence . Proc. Royal Soc. London, , 261 : 209 – 215 .
   PubMed Web of Science ®Google Scholar
• Miller , B. 1993 . Preventive therapy for tuberculosis . Medical Clinics of North America, , 77 : 1263 – 1275 .
   PubMed Web of Science ®Google Scholar
• Naresh , R. and Tripath , A. 2005 . Modelling and analysis of HIV‐TB co‐infection in a variable size population . Math. Model. Anal., , 10 : 275 – 286 .
   Google Scholar
• Nowak , M.A. and Sigmund , K. 2002 . “ Super‐and coinfection: The two extremes ” . In Adaptive dynamics of infectious diseases: In pursuit of virulence management , Cambridge University Press .
   Google Scholar
• World Health Organisation . 2000 . “ Anti‐tuberculosis drug resistance in the world in people living with HIV ” . In Prevalence and trends , Geneva : WHO . Report 2
   Google Scholar
• Shilov , M.V. and Dye , C. 2001 . The resurgence of tuberculosis in Russia . Philos Trans R Soc Lond Bio Sci, , 356 : 1069 – 1075 .
   PubMedGoogle Scholar
• Singh , J. 2007 . Isolating TB patients: prevention better than cure , SciDevNet .
   Google Scholar