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A TB model: Is disease eradication possible in India?

1. Public Health Foundation of India, Plot No. 47, Sector-44, Gurgaon-122002, Haryana, India
2. Dipartimento di Matematica "Giuseppe Peano", Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy

Tuberculosis (TB) is returning to be a worldwide global public health threat. It is estimated that 9.6 million cases occurred in 2014, of which just two-thirds notified to public health authorities. The "missing cases" constitute a severe challenge for TB transmission control. TB is a severe disease in India, while, worldwide, the WHO estimates that one third of the entire world population is infected.

Nowadays, incidence estimation relies increasingly more on notifications of new cases from routine surveillance. There is an urgent need for better estimates of the load of TB, in high-burden settings. We developed a simple model of TB transmission dynamics, using a dynamical system model, consisting of six classes of individuals. It contains the current medical epidemiologists' understanding of the spread of the Mycobacterium tuberculosis in humans, which is substantiated by field observations at the district level in India. The model incorporates the treatment options provided by the public and private sectors in India. Mathematically, an interesting feature of the system is that it exhibits a backward, or subcritical, bifurcation.

One of the results of the investigation shows that the discrepancy between the diagnosis rates of the public and private sector does not seem to be the cause of the endemicity of the disease, and, unfortunately, even if they reached 100% of correct diagnosis, this would not be enough to achieve disease eradication.

Several other approaches have been attempted on the basis of this model to indicate possible strategies that may lead to disease eradication, but the rather sad conclusion is that they unfortunately do not appear viable in practice.

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Keywords Disease latency; basic reproduction number; public hospitalization; private hospitalization; backward bifurcation; subcritical bifurcation

Citation: Surabhi Pandey, Ezio Venturino. A TB model: Is disease eradication possible in India?. Mathematical Biosciences and Engineering, 2018, 15(1): 233-254. doi: 10.3934/mbe.2018010


  • [1] M. A. Behr,S. A. Warren,H. Salomon,P. C. Hopewell,A. P. de Leon,C. L. Daley,P. M. Small, Transmission of mycobacterium tuberculosis from patients smear-negative for acid-fast bacilli, Lancet, 353 (1999): 444-449.
  • [2] S. Bernardi and E. Venturino, Viral epidemiology of the adult Apis Mellifera infested by the Varroa destructor mite, Heliyon, 2.
  • [3] V. Chadha, S. Majhi, S. Nanda and S. Pandey, Prediction of prevalence and incidence of tuberculosis in a district in India, submitted.
  • [4] V. K. Chadha, P. Kumar, S. M. Anjinappa, S. Singh, S. Narasimhaiah, M. V. Joshi, J. Gupta, Lakshminarayana, J. Ramchandra, M. Velu, S. Papkianathan, S. Babu and H. Krishna, Prevalence of pulmonary tuberculosis among adults in a rural sub-district of South India, PLoS ONE, 7.
  • [5] V. K. Chadha,R. Sarin,P. Narang,K. R. John,K. K. Chopra,R. J. D.K Mendiratta,V. Vohra,A. N. hashidhara,G. Muniraj,P. G. Gopi,P. Kumar, Trends in the annual risk of tuberculous infection in India, International Journal of Tuberculosis and Lung Disease, 17 (2013): 312-319.
  • [6] G. W. Comstock,V. T. Livesay,S. F. Woolpert, The prognosis of a positive tuberculin reaction in childhood and adolescence, American J of Epidemiology, 99 (1974): 131-138.
  • [7] E. L. Corbett,C. J. Watt,N. Walker,D. Maher,B. G. Williams,M. C. Raviglione,C. Dye, The growing burden of tuberculosis: Global trends and interactions with the HIV epidemic, JAMA Internal Medicine, Formerly known as Archives of Internal Medicine, 163 (2003): 1009-1021.
  • [8] D. W. Dowdy,R. E. Chaisson, The persistence of tuberculosis in the age of dots: Reassessing the effect of case detection, Bulletin World Health Organisation, 87 (2009): 296-304.
  • [9] S. H. Fercbee, Controlled chemoprophylaxis trials in tuberculosis. a general review, Bibliotheca Tuberculosea, 26 (1970): 28-106.
  • [10] K. Floyd,V. K. Arora,K. J. R. Murthy,K. Lonnroth,N. Singla,Y. Akbar,M. Zignol,M. Uplekar, Cost-effectiveness of PPM-DOTS in India, Bulletin of the World Health Organization, 84 (2006): 437-439.
  • [11] P. G. Gopi,R. Subramani,K. Sadacharam,P. R. Narayanan, Yield of pulmonary tuberculosis cases by employing two screening methods in a community survey, International Jounral of Tuberculosis and Lung Disease, 10 (2006): 343-345.
  • [12] M. Martcheva, null, An Introduction to Mathematical Epidemiology, Springer-Verlag, New York, 2015.
  • [13] S. Martorano Raimundo, E. Venturino, Drug resistant impact on tuberculosis transmission, Wseas Transactions on Biology and Biomedicine, v. 5, 85-95, ISSN 1109-9518,2008.
  • [14] S. Martorano Raimundo,H. M. Yang,E. Venturino, Theoretical assessment of the relative incidences of sensitive and resistant Tuberculosis epidemic in presence of drug treatment, Mathematical Biosciences and Engineering, 11 (2014): 971-993.
  • [15] R. Naresh,S. Pandey,J. B. Shukla, Modeling the cumulative cffect of ecological factors in the habitat on the spread of tuberculosis, International Journal of Biomathematics, 2 (2009): 339-355.
  • [16] W. H. Organization, World health organization global TB report 2016,2016, URL http://www.who.int/tb/publications/global_report/gtbr2016_executive_summary.pdf?ua=1, Accessed online 20-January-2017.
  • [17] W. H. Organization, World health organization tb report 2015,2016, URL http://www.who.int/tb/publications/global_report/gtbr15_main_text.pdf, Accessed online 20-January-2017.
  • [18] S. Pandey,V. K. Chadha,R. Laxminarayan,N. Arinaminpathy, Estimating tuberculosis incidence from primary survey data: A mathematical modeling approach, International Journal of TB and Lung Disease, 21 (2017): 366-374.
  • [19] S. Pandey, S. Nanda and P. S. Datti, Mathematical analysis of TB model pertaining to India, Submitted.
  • [20] A. Perasso, An introduction to the basic reproduction number in mathematical biology, private communication.
  • [21] I. Registrar General, Sample registration survey bulletin, 2011, December 2011, URL http://censusindia.gov.in/vital_statistics/SRS_Bulletins/Bulletins.aspx.
  • [22] S. Satyanarayana, S. A. Nair, S. S. Chadha, R. Shivashankar, G. Sharma, S. Yadav, S. Mohanty, V. Kamineni, C. Wilson, A. D. Harries and P. K. Dewan, From where are tuberculosis patients accessing treatment in India? results from a cross-sectional community based survey of 30 districts, PLoS One, 16.
  • [23] V. Sophia,V. H. Balasangameswara,P. S. Jagannatha,V. N. Saroja,P. Kumar, Treatment outcome and two and half years follow-up status of new smear positive patients treated under RNTCP, Indian Journal of Tuberculosis, 51 (2004): 199-208.
  • [24] K. Styblo, The relationship between the risk of tuberculous infection and the risk of developing infectious tuberculosis, Bulletin of the International Union Against Tuberculosis and Lung Disease, 60 (1985): 117-129.
  • [25] R. Subramani,S. Radhakrishna,T. R. Frieden,C. K. P. G. Gopi,T. Santha,F. Wares,N. Selvakumar,P. R. Narayanan, Rapid decline in prevalence of pulmonary tuberculosis after dots implementation in a rural area of South India, International Jounral of Tuberculosis and Lung Disease, 12 (2008): 916-920.
  • [26] A. Thomas,P. G. Gopi,T. Santha,V. Chandrasekaran,R. Subramani,N. Selvakumar,S. I. Eusuff,K. Sadacharam,P. R. Narayanan, Predictors of relapse among pulmonary tuberculosis patients treated in a dots programme in South India, International Journal of Tuberculosis and Lung Disease, 9 (2005): 556-561.
  • [27] M. Uplekar,S. Juvekar,S. Morankar,S. Rangan,P. Nunn, Tuberculosis patients and practitioners in private clinics in India, International Journal of Tuberculosis and Lung Disease, 6 (1998): 324-329.
  • [28] M. W. Uplekar,S. K. Jvekar,D. B. Parande, Tuberculosis management in private practice and its implication, Indian Journal of Tuberculosis, 43 (1996): 19-22.
  • [29] P. van den Driessche,J. Watmough, A simple sis epidemic model with a backward bifurcation, J. of Mathematical Biology, 40 (2000): 525-540.
  • [30] P. van den Driessche,J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002): 29-48.
  • [31] F. van Leth,M. J. van der Werf,M. W. Borgdorff, Prevalence of tuberculous infection and incidence of tuberculosis: A re-assessment of the styblo rule, Bulletin of the World Health Organization, 86 (2008): 20-26.


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