Search Advanced

Mathematical Biosciences and Engineering

2014, Volume 11, Issue 4: 971-993. doi: 10.3934/mbe.2014.11.971
Previous Article Next Article

Theoretical assessment of the relative incidences of sensitive andresistant tuberculosis epidemic in presence of drug treatment

  • 1.
    Faculdade de Medicina da Universidade de São Paulo, Disciplina de Informática Médica and LIM01-HCFMUSP, Rua Teodoro Sampaio, 115, CEP: 05405-000, São Paulo, SP
  • 2.
    Universidade de Campinas, IMECC, DMA, Praça Sérgio Buarque de Holanda, 651, Campinas, SP
  • 3.
    Università di Torino, Dipartimento di Matematica "Giuseppe Peano", Via Carlo Alberto 10, 10123 Torino
  • Received: 01 August 2013 Accepted: 29 June 2018 Published: 01 March 2014

  • MSC : Primary: 92D30; Secondary: 92C50.

  • Despite the availability of effective treatment, tuberculosis (TB)remains a major global cause of mortality.Multidrug-resistant tuberculosis (MDR-TB) is a form of TB thatis resistant to at least two drugs used for the treatment of TB,and originally is developed when a case of drug-susceptibleTB is improperly or incompletely treated.This work is concerned with a mathematical model to evaluate the effect ofMDR-TB on TB epidemic and its control.The model assessing the transmission dynamics of both drug-sensitive anddrug-resistant TB includes slow TB(cases that result from endogenous reactivation of susceptible andresistant latent infections). We identify the steady states of the model toanalyse their stability.We establish threshold conditions for possible scenarios:elimination of sensitive and resistant strains and coexistence of both.We find that the effective reproductive number iscomposed of two critical values, relative reproductive number for drug-sensitiveand drug-resistant strains.Our results imply that thepotential for the spreading of the drug-resistant strain should be evaluated withinthe context of several others factors.We have also found that even the considerably less fit drug-resistant strainscan lead to a high MDR-TB incidence, because the treatment is less effective against them.

    Citation: Silvia Martorano Raimundo, Hyun Mo Yang, Ezio Venturino. Theoretical assessment of the relative incidences of sensitive andresistant tuberculosis epidemic in presence of drug treatment[J]. Mathematical Biosciences and Engineering, 2014, 11(4): 971-993. doi: 10.3934/mbe.2014.11.971

    Related Papers:

  • Despite the availability of effective treatment, tuberculosis (TB)remains a major global cause of mortality.Multidrug-resistant tuberculosis (MDR-TB) is a form of TB thatis resistant to at least two drugs used for the treatment of TB,and originally is developed when a case of drug-susceptibleTB is improperly or incompletely treated.This work is concerned with a mathematical model to evaluate the effect ofMDR-TB on TB epidemic and its control.The model assessing the transmission dynamics of both drug-sensitive anddrug-resistant TB includes slow TB(cases that result from endogenous reactivation of susceptible andresistant latent infections). We identify the steady states of the model toanalyse their stability.We establish threshold conditions for possible scenarios:elimination of sensitive and resistant strains and coexistence of both.We find that the effective reproductive number iscomposed of two critical values, relative reproductive number for drug-sensitiveand drug-resistant strains.Our results imply that thepotential for the spreading of the drug-resistant strain should be evaluated withinthe context of several others factors.We have also found that even the considerably less fit drug-resistant strainscan lead to a high MDR-TB incidence, because the treatment is less effective against them.


    加载中
    [1] PLoS Medicine, 3 (2006), e124.
    [2] Academic, New York, 1979.
    [3] Bulletin of Mathematical Biology, 71 (2009), 1745-1780.
    [4] Nature Medicine, 10 (2004), 1111-1116.
    [5] Science, 273 (1996), 497-500.
    [6] Nature Medicine, 1 (1995), 815-821.
    [7] Journal of Molecular Medicine, 76 (1998), 624-636.
    [8] Emerging Infectious Diseases, 10 (2004), 1523-1528.
    [9] The International Journal of Tuberculosis and Lung Disease, 13 (2009), 1456-1466.
    [10] Clinical Infectious Diseases, 33 (2001), e42-e47.
    [11] Nonlinear Dynamics, 67 (2012), 2027-2051.
    [12] MMWR, 34 (1985), 429-431.
    [13] Nature Medicine, 10 (2004), 1117-1121.
    [14] PLos ONE, 3 (2008), e2363.
    [15] PLos ONE, 6 (2011), e18327.
    [16] Bulletin of Mathematical Biology, 71 (2009), 247-263.
    [17] American Review of Respiratory Disease, 121 (1980), 313-316.
    [18] BMC Infectious Diseases, 10 (2010),349 http://www.biomedcentral.com/1471-2334/10/349.
    [19] Proceedings of the Royal Society of London B, 268 (2001), 45-52.
    [20] Tuberculosis, 83 (2003), 44-51.
    [21] Math. Biosc., 167 (2000), 51-64.
    [22] SIAM Journal on Applied Mathematics, 62 (2002), 1634-1656.
    [23] Archives of Internal Medicine, 160 (2000), 630-636.
    [24] Proceedings of the Royal Society B, 271 (2004), 617-623.
    [25] 2nd Ed. krieger, Basel, 1980.
    [26] SIAM Review, 42 (2000), 599-653.
    [27] in D. Mollison (Ed.), Epidemic Models: Their Structure and Relation to Data, Cambridge University, Cambridge, 5 (1994), p. 84.
    [28] Discrete Dynamics in Nature and Society, 2011.
    [29] PLos ONE, 3 (2008), e1839.
    [30] The New England Journal of Medicine, 315 (1986), 1570-1575.
    [31] Journal of Theoretical Biology, 269 (2011), 31-45.
    [32] Infection and Immunity, 63 (1995), 741-743.
    [33] BioSystems, 108 (2012), 1-13.
    [34] Journal of Biological Systems, 10 (2002), 61-83.
    [35] Systems Analysis Modelling Simulation, 43 (2003), 423-442.
    [36] Biosystems, 99 (2010), 215-222.
    [37] The International Journal of Tuberculosis and Lung Disease, 5 (2001), 339-354.
    [38] Theoretical Population Biology, 71 (2007), 196-212.
    [39] Journal of Theoretical Biology, 280 (2011), 88-100.
    [40] Journal of Biological Dynamics, 2 (2008), 323-345.
    [41] The New England Journal of Medicine, 328 (1993), 1137-1144.
    [42] The American Review of Respiratory Disease, 132 (1985), 125-132.
    [43] Am J Epidemiol, 178 (2013), 508-520.
    [44] The International Journal of Tuberculosis and Lung Disease, 5 (2001), 321-328.
    [45] http://www.who.int/tb/publications/2011/factsheet_tb_2011.pdf (accessed in September, 2012).
    [46] WHO/CDS/TB/2000/.278 The WHO/IUATLD Global Project on Anti-Tuberculosis Drug Resistance Surveillance. Report 2. World Health Organization, Geneva, Switzerland (2000).
    [47] Fact sheet N. 104, March 2012. (accessed in September, 2012).
  • Reader Comments
  • © 2014 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
2.6 3.9

Metrics

Article views(1913) PDF downloads(492) Cited by(9)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog