Russian version English version
Volume 2   Issue 2   Year 2007
Avilov K.K., Romanyukha A.A.

Mathematical Models of Tuberculosis Extension and Control of it

Mathematical Biology & Bioinformatics. 2007;2(2):188-318.

doi: 10.17537/2007.2.188.

References

  1. Waaler HT, Geser A, Andersen S. The use of mathematical models in the study of the epidemiology of tuberculosis. Am. J. publ. Health. 1962;52:1002-1013.
  2. Waaler HT. Cost-benefit analyses of BCG vaccination under various epidemiological situations. Bull. int. Union Tuberc. 1968;41:42-52.
  3. Waaler HT. A Dynamic Model for the Epidemiology of Tuberculosis. American Review of Respiratory Disease. 1968;98:591-600.
  4. Waaler HT, Piot MA. The use of an epidemiological model for estimationg the effectiveness of tuberculosis control measures. Sensitivity of the effectiveness of tuberculosis control measures to the coverage of the population. Bulletin of the World Health Orga-nization. 1969;41:75-93.
  5. Waaler H.T., Piot M.A. Use of an Epidemiological Model for Estimating the Effectiveness of Tuberculosis Control Measures. Sensitivity of the Effectiveness of Tuberculosis Control Measures to the Social Time Preference. Bulletin of the World Health Organization. 1970;43:1-16.
  6. Waaler HT, Gothi GD, Baily GVJ, Nair SS. Tuberculosis in rural South India. A study of possible trends and the potential impact of antituberculosis programmes. Bulletin of the World Health Organization. 1974;51:263-271.
  7. Brogger S. Systems analysis in tuberculosis control: A model. American Review of Respiratory Disease. 1967;95(3):419-434.
  8. ReVelle CS, Lynn WR, Feldmann F. Mathematical models for the economic allocation of tuberculosis control activities in developing nations. American Review of Respiratory Disease. 1967;96:893-909.
  9. ReVelle C.S. The Economic Allocation of Tuberculosis Control Activities in Developing Nations. Thesis. Cornell University; 1967.
  10. Hedrich AW. Monthly Estimates of the Child Population "Susceptible" to Measles, 1900-1931, Baltimore. Md. Am. J. Hyg. 1933;17:613-636.
  11. Muench H. Catalytic Models in Epidemiology. Cambridge, Mass.: Harvard University Press; 1959. doi: 10.4159/harvard.9780674428928
  12. Frost WH. How Much Control of Tuberculosis? A.J.P.H. 1937;27:759.
  13. Feldman FM. How Much Control of Tuberculosis: 1937-1957-1977? Am. J. Public Health Nations Health. 1957;47(10):1235-1241. doi: 10.2105/AJPH.47.10.1235
  14. Palmer CE, Shaw LW, Comstock GW. Community trials of BCG vaccination. Am. Rev. Tuberc. 1958;77:877.
  15. Sutherland I. An Estimation of the Scope for BCG Vaccination in Preventing Tuberculosis Among Those Aged 15-19 Years in Englsnd and Wales at the present time. Tubercle. 1959;40:413. doi: 10.1016/S0041-3879(59)80096-9
  16. Frimodt-Møller JA. Community-Wide tuberculosis Study in a South Indian Rural Population, 1950-1955. Bull World Health Organ. 1960;22:61.
  17. Ferebee SH. An epidemiological model of tuberculosis in the United States. Bulletin of the National Tuberculosis Association. 1967;4:7.
  18. Narain R, Nair SS, Naganna K, Chandrasekhar P, Rao GR, Lal P. Problems in defining a “case” of pulmonary tuberculosis in prevalence surveys. Bulletin of the World Health Organization. 1968;39:701.
  19. National Tuberculosis Institute, Bangalore. Tuberculosis in a rural population of South India: a five-year epidemiological study. Bulletin of the World Health Organization. 1974;51:473-488.
  20. Azuma Y. A simple simulation model of tuberculosis epidemiology for use without largescale computers. Bulletin of the World Health Organization. 1975;52:313-322.
  21. Styblo K, Bumgarner JR. Tuberculosis can be controlled with existing technologies: evidence. The Hague: Tuberculosis Surveillance Research Unit Progress Report; 1991. P. 60-72.
  22. The Stop TB Strategy. World Health Organization; 2006. WHO/HTM/STB/2006.37.
  23. Blower SM, McLean AR, Porco TC, Small PM, Hopewell PC, Sanchez MA, Moss AR. The intrinsic transmission dynamics of tuberculosis epidemics. Nature Medcine. 1995;1(8):815-821. doi: 10.1038/nm0895-815
  24. Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control. Oxford Science Publications; 1992.
  25. Blower SM, Small PM, Hopewell PC. Control strategies for tuberculosis: new models for old problems. Science. 1996;273:497-500. doi: 10.1126/science.273.5274.497
  26. Lietman T, Porco T, Blower S. Leprosy and tuberculosis: the epidemiological consequences of cross-immunity. American Journal of Public Health. 1997;87(12):1923-1927. doi: 10.2105/AJPH.87.12.1923
  27. Lechat MF. The torments and blessings of the leprosy epidemiometric model. Lepr. Rev. 1981;52:187-196.
  28. Abel L, Mallet A, Demenais F, Booney GE. Modeling the age-of-onset function in segregation analysis: a casual scheme for leprosy. Genet. Epidemiol. 1989;6:501-516.
  29. Porco TC, Blower SM. Quantifying the Intrinsic Transmission Dynamics of Tuberculosis. Theoretical Population Biology. 1998;54:117-132. doi: 10.1006/tpbi.1998.1366
  30. Blower SM, Gerberding JL. Understanding, predicting and controlling the emergence of drug-resistant tuberculosis: a theoretical framework. J. Mol. Med. 1998;76:624-636.
  31. Blower S, Porco T, Lietman T. Tuberculosis: The Evolution of Antibiotic Resistance and the Design of Epidemic Control Strategies. In: Horn, Simonett, Webb. Mathematical Models in Medical and Health Sciences. USA: Vanderbilt Press; 1998.
  32. Ziv E, Daley CL, Blower SM. Early Therapy for Latent Tuberculosis Infection. American Journal of Epidemiology. 2001;153(4):381-385. doi: 10.1093/aje/153.4.381
  33. Lietman T, Blower SM. Potential Impact of Tuberculosis Vaccines as Epidemic Control Agents. Clinical Infectious Diseases. 2000;30(3):S316-S322. doi: 10.1086/313881
  34. Ziv E, Daley CL, Blower S. Potential Public Health Impact of New Tuberculosis Vaccines. Emerging Infectious Diseases. 2004;10(9):1529-1535. doi: 10.3201/eid1009.030921
  35. Porco TC, Small PM, Blower SM. Amplification Dynamics: Predicting the Effect of HIV on Tuberculosis Outbreaks. Journal of Aquired Immune Deficiency Syndromes. 2001;28:437-444. doi: 10.1097/00042560-200112150-00005
  36. Blower SM, Chou T. Modeling the emergence of the ‘hot zones’: tuberculosis and the amplification dynamics of drug resistance. Nature Medcine. 2004;10(10):1111-1116. doi: 10.1038/nm1102
  37. Feng Z, Castillo-Chavez C, Capurro AF. A Model for Tuberculosis with Exogenous Reinfection. Theoretical Population Biology. 2000;57:235-247. doi: 10.1006/tpbi.2000.1451
  38. Blower SM, Daley CL. Problems and solutions for the Stop TB partnership. The Lancet Infectious Diseases. 2002;2:374-376. doi: 10.1016/S1473-3099(02)00292-X
  39. Sutherland I, Svandova E. Endogenous reactivation and exogenous infection their relative importance with regard to the development of non-primary tuberculosis. Bulletin of the World Health Organization. 1972;47:123.
  40. Sutherland I, Svandova E, Radhakrishna S. The development of clinical tuberculosis following infection with tubercle bacilli. Tubercle. 1982;63:255-268. doi: 10.1016/S0041-3879(82)80013-5
  41. Vynnycky E. An Investigation of the Transmission Dynamics of M. tuberculosis: PhD thesis. University of London; 1996.
  42. Vynnycky E, Fine PEM. The natural history of tuberculosis: the implications of agedependent risks of disease and the role of reinfection. Epidemiol. Infect. 1997;119:183-201.
  43. Vynnycky E, Fine PEM. Lifetime Risks, Incubation Period, and Serial Interval of Tuberculosis. American Journal of Epidemiology. 2000;152(3):247-263. doi: 10.1093/aje/152.3.247
  44. Vynnycky E, Nagelkerke N, Borgdorff MW, van Soolingen D, van Embden JD, Fine PEM. The effect of age and study duration on the relationship between ’clustering’ of DNA fingerprint patterns and the proportion of tuberculosis disease attributable to recent transmission. Epidemiol Infect. 2001;126(1):43-62.
  45. Vynnycky E, Borgdorff MW, van Soolingen D, Fine PEM. Annual Mycobacterium tuberculosis infection risk and interpretation of clustering statistics. Emerging Infectious diseases. 2003;9(2):176-183. doi: 10.3201/eid0902.010530
  46. Holm J. Development of tuberculous infection to tuberculous disease. The Hague, The Netherlands: TSRU Progress Report; KNCV; 1969.
  47. Vynnycky E, Fine PEM. The annual risk if infection with Mycobacterium tuberculosis in England and Wales since 1901. Int. J. Tuberc. Lung Dis. 1997;1:389-82.
  48. Sutherland I. The ten-year incidence of clinical tuberculosis following “conversion” in 2550 individuals aged 14 to 19 years. The Hague, The Netherlands: TSRU Progress Report; KNCV; 1968.
  49. Castillo-Chavez C, Feng Z. To treat or not to treat: the case of tuberculosis. J. Math. Biol. 1997;35:629-656.
  50. Castillo-Chavez C, Feng Z. Global stability of an age-structure model for TB and its applications to optimal vaccination strategies. Mathematical Biosciences. 1998;151:135-154. doi: 10.1016/S0025-5564(98)10016-0
  51. CastilloChavez C, Feng Z. Mathemetical models for the disease dynamics of tuberculosis. In: Advances in Mathematical Population Dynamics Molecules, Cells, and Man. Eds. O. Arino, D. Axelrod, M. Kimmel. World Scientifc Press; 1998. P. 629-656.
  52. Mena-Lorca J, Velasco-Hernandez JX, Castillo-Chavez C. Density-dependent dynamics and superinfection in an epidemic model. IMA Journal of Mathematics Applied in Medicine and Biology. 1999;16:307-317. doi: 10.1093/imammb/16.4.307
  53. Aparicio JP, Capurro AF, Castillo-Chavez C. Transmission and Dynamics of Tuberculosis on Generalized Households. J. theor. Biol. 2000;206:327-341.
  54. Aparicio JP, Capurro AF, Castillo-Chavez C. On the fall and rise of tuberculosis. Technical Report Series, BU-1477-M, Department of Biometrics, Cornell University; 2000.
  55. Feng Z, Huang W, Castillo-Chavez C. On the role of variable latent periods in mathematical models for tuberculosis. Journal of Dynamics and Differential Equations. 2001;13(2):425-452. doi: 10.1023/A:1016688209771
  56. Song B, Castillo-Chavez C, Aparicio JP. Tuberculosis models with fast and slow dynamics: the role of close and casual contacts. Mathematical Biosciences. 2002;180:187-205. doi: 10.1016/S0025-5564(02)00112-8
  57. Castillo-Chavez C, Song B. An Overview of Dynamical Models of Tuberculosis. Technical Report of BSCB, Cornell University, Ithaca, BU-1607-M; 2002.
  58. Song B, Castillo Chavez C, Aparicio JP. Global Dynamics of Tuberculosis Models with Density Dependent Demography. In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods and Theory. Eds. Castillo Chavez C, Pauline van den Driessche P, Denise Kirschner D, Yakubu AA. Berlin Heidelberg New York: Springer Veralg; 2002. V. 126. P. 275-294. doi: 10.1007/978-1-4613-0065-6_16
  59. Aparicio JP, Capurro AF, Castillo-Chavez C. Markers of Disease Evolution: The Case of Tuberculosis. J. theor. Biol. 2002;215:227-237.
  60. Aparicio JP, Capurro AF, Castillo Chavez C. Longterm Dynamics and Reemergence of Tuberculosis. In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction. Eds. Blower S, Castillo Chavez C, Kirschner D, van den Driessche P, Aziz Yakubu A. Springer Verlag; 2002. P. 351-360. doi: 10.1007/978-1-4757-3667-0_20
  61. Castillo-Chavez C, Song B. Dynamic models of tuberculosis and their applications. Mathematical Biosciences and Engineering. 2004;1(2):361-404. doi: 10.3934/mbe.2004.1.361
  62. Feng Z, Ianelli M, Milner FA. A Two-Strain Tuberculosis ModelWith Age of Infection. SIAM J. APPL. MATH. 2002;62(5):1634-1656.
  63. Dye C, Garnett GP, Sleeman K, Williams BG. Prospects for worldwide tuberculosis control under the WHO DOTS strategy. The Lancet. 1998;352:1886-1891. doi: 10.1016/S0140-6736(98)03199-7
  64. Baltussen R, Floyd K, Dye C. Cost effectiveness analysis of strategies for tuberculosis control in developing countries. BMJ. 2005;331(7529):1364. doi: 10.1136/bmj.38645.660093.68
  65. Williams BG, Granich R, Chauhan LS, Dharmshaktu NS, Dye C. The impact of HIV AIDS on the control of tuberculosis in India. PNAS. 2005;102(27):9619-9624. doi: 10.1073/pnas.0501615102
  66. Stover J. TB-HIV spreadsheet model. A model for illustrating the effects of the HIV epidemics on tuberculosis. Washington, DC: Futures Group International, the POLICY project; 1998.
  67. Styblo K, Broekmans JF, Borgdorff MW. Expected decrease in tuberculosis incidence during the elimination phase. How to determine its trend? Tuberculosis Surveillance and Research Unit Progress Report 1997. The Hague, Royal Netherlands Tuberculosis Association. (KNCV).
  68. Dye C, Williams BG. Criteria for the control of drug-resistant tuberculosis. Proc. Natl. Acad. Sci. USA. 2000;97(14):8180-8185. doi: 10.1073/pnas.140102797
  69. Dye C, Espinal MA. Will tuberculosis become resistant to all antibiotics? Proc. R. Soc. Lond. B. Biol. Sci. 2001;268:45-52.
  70. Anti-Tuberculosis Drug Resistance in the World. Report No. 2. Geneva: World Health Organization. 2000. WHO/CDS/TB/2000.278.
  71. Currie CS, Williams BG, Cheng RC, Dye C. Tuberculosis epidemics driven by HIV: is prevention better than cure? AIDS. 2003;17(17):2501-2508. doi: 10.1097/00002030-200311210-00013
  72. Currie CS, Floyd K, Williams BG, Dye C. Cost, affordability and cost-effectiveness of strategies to control tuberculosis in countries with high HIV prevalence. BMC Public Health. 2005;5:130. doi: 10.1186/1471-2458-5-130
  73. Murray CJL, Salomon JA. Modeling the impact of global tuberculosis control strategies. Proc. Natl. Acad. Sci. USA. 1998;95:13881-3886. (Medical Sciences). doi: 10.1073/pnas.95.23.13881
  74. Murray CJL, Salomon JA. Using mathematical models to evaluate global tuberculosis control strategies. Cambridge, MA: Harvard Center for Population and Development Studies; 1998.
  75. Cohen T, Murray M. Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness. Nature Medcine. 2004;10(10):1117-1121. doi: 10.1038/nm1110
  76. Resch SC, Salomon JA, Murray M, Weinstein MC. Cost-effectiveness of treating multidrug-resistant tuberculosis. PLoS Medcine. 2006;3(7):1048-1057.
  77. Salomon JA, Lloyd-Smith JO, Getz WM, Resch S, Sanchez MS, Porco TC, Borgdorff MW. Prospects for advancing tuberculosis control efforts through novel therapies. PloS Medcine. 2006;3(8):1302-1309.
  78. Regiony Rossii. Osnovnye kharakteristiki sub''ektov RF (Regions of Russia. The Main Characteristics of the Constituent Territories of the Russian Federation): Statistical composite book. Moscow; 2004 (in Russ.).
  79. Perelman MI, Marchuk GI, Borisov SE, Kazennukh BYa, Avilov KK, Karkach AS, Romanyukha AA. Tuberculosis epidemiology in Russia: the mathematical model and data analysis. Russ. J. Numer. Anal. Math. Modelling. 2004;19(4):305-314.
  80. Avilov KK, Romanyukha AA. Mathematical Modeling of Tuberculosis Propagation and Patient Detection. Automation and Remote Control. 2007;68(9):1604-1617. doi: 10.1134/S0005117907090159
Table of Contents Original Article
Math. Biol. Bioinf.
2007;2(2):188-318
doi: 10.17537/2007.2.188
published in Russian

Abstract (rus.)
Abstract (eng.)
Full text (rus., pdf)
References

 

  Copyright IMPB RAS © 2005-2024