Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis

D.P. Moualeu; S. Bowong; J.J. Tewa; Y. Emvudu

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 3, page 117-146
  • ISSN: 0973-5348

Abstract

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Tuberculosis (TB) remains a major global health problem. A possible risk factor for TB is diabetes (DM), which is predicted to increase dramatically over the next two decades, particularly in low and middle income countries, where TB is widespread. This study aimed to assess the strength of the association between TB and DM. We present a deterministic model for TB in a community in order to determine the impact of DM in the spread of the disease. The important mathematical features of the TB model are thoroughly investigated. The epidemic threshold known as the basic reproduction number and equilibria for the model are determined and stabilities analyzed. The model is numerically analyzed to assess the impact of DM on the transmission dynamics of TB. We perform sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Numerical simulations suggest that DM enhances the TB transmission and progression to active TB in a community. The results suggest that there is a need for increased attention to intervention strategies such as the chemoprophylaxis of TB latent individuals and treatment of active TB in people with DM, which may include testing for suspected diabetes, improved glucose control, and increased clinical and therapeutic monitoring in order to reduce the burden of the disease.

How to cite

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Moualeu, D.P., et al. "Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis." Mathematical Modelling of Natural Phenomena 7.3 (2012): 117-146. <http://eudml.org/doc/222424>.

@article{Moualeu2012,
abstract = {Tuberculosis (TB) remains a major global health problem. A possible risk factor for TB is diabetes (DM), which is predicted to increase dramatically over the next two decades, particularly in low and middle income countries, where TB is widespread. This study aimed to assess the strength of the association between TB and DM. We present a deterministic model for TB in a community in order to determine the impact of DM in the spread of the disease. The important mathematical features of the TB model are thoroughly investigated. The epidemic threshold known as the basic reproduction number and equilibria for the model are determined and stabilities analyzed. The model is numerically analyzed to assess the impact of DM on the transmission dynamics of TB. We perform sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Numerical simulations suggest that DM enhances the TB transmission and progression to active TB in a community. The results suggest that there is a need for increased attention to intervention strategies such as the chemoprophylaxis of TB latent individuals and treatment of active TB in people with DM, which may include testing for suspected diabetes, improved glucose control, and increased clinical and therapeutic monitoring in order to reduce the burden of the disease. },
author = {Moualeu, D.P., Bowong, S., Tewa, J.J., Emvudu, Y.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {nonlinear dynamical systems; epidemiological models; diabetes; tuberculosis; stability; bifurcation; bifurcations},
language = {eng},
month = {6},
number = {3},
pages = {117-146},
publisher = {EDP Sciences},
title = {Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis},
url = {http://eudml.org/doc/222424},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Moualeu, D.P.
AU - Bowong, S.
AU - Tewa, J.J.
AU - Emvudu, Y.
TI - Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/6//
PB - EDP Sciences
VL - 7
IS - 3
SP - 117
EP - 146
AB - Tuberculosis (TB) remains a major global health problem. A possible risk factor for TB is diabetes (DM), which is predicted to increase dramatically over the next two decades, particularly in low and middle income countries, where TB is widespread. This study aimed to assess the strength of the association between TB and DM. We present a deterministic model for TB in a community in order to determine the impact of DM in the spread of the disease. The important mathematical features of the TB model are thoroughly investigated. The epidemic threshold known as the basic reproduction number and equilibria for the model are determined and stabilities analyzed. The model is numerically analyzed to assess the impact of DM on the transmission dynamics of TB. We perform sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Numerical simulations suggest that DM enhances the TB transmission and progression to active TB in a community. The results suggest that there is a need for increased attention to intervention strategies such as the chemoprophylaxis of TB latent individuals and treatment of active TB in people with DM, which may include testing for suspected diabetes, improved glucose control, and increased clinical and therapeutic monitoring in order to reduce the burden of the disease.
LA - eng
KW - nonlinear dynamical systems; epidemiological models; diabetes; tuberculosis; stability; bifurcation; bifurcations
UR - http://eudml.org/doc/222424
ER -

References

top
  1. Global tuberculosis report. Geneva : World Health Organization ; Available from : [accessed 25 March 2011], 2010.  URIhttp://whqlibdoc.who.int/publications/2010/9789241564069-eng.pdf
  2. C. Dye, B.G. Williams. The population dynamics and control of tuberculosis. Science328 (2010), 856–861.  
  3. K. Lönnroth, K.G. Castro, J.M. Chakaya, L.S. Chauhan, K. Floyd. Tuberculosis control and elimination 2010–50 : cure, care, and social development. Lancet375 (2010), 1814-1829.  
  4. J. Stephenson. TB progress slowing. JAMA299 (2008), 1764-1771, doi : .  URI10.1001/jama.299.15.1764-b
  5. The World Health Report, Diabetes, Fact sheet N0 312, , Jan. 2011.  URIhttp://www.who.int/mediacentre/factsheets/fs312/en/
  6. American Diabetes Association. Diagnosis and classification of diabetes mellitus. Diabetes Care 32 (2008), 62–67.  
  7. Diabetes atlas. Brussels, International Diabetes Federation ; Available from : 2010, [accessed 25 March 2011].  URIhttp://www.diabetesatlas.org/
  8. C. Dye. Global epidemiology of tuberculosis. Lancet367 (2006), 938–940, doi : PMID :16546542.  URI10.1016/S0140-6736(06)68384-0
  9. P.N. Oscarsson, H. Silwer. Incidence of pulmonary tuberculosis among diabetics. Acta Med. Scand.335 (1958), 23–48.  
  10. H.F. Root. The association of diabetes and tuberculosis. N. Engl. J. Med.210 (1934), 1–13. doi :.  URI10.1056/NEJM193401042100101
  11. S.J. Kim, Y.P. Hong, W.J. Lew, S.C. Yang, E.G. Lee. Incidence of pulmonary tuberculosis among diabetics. Tuber. Lung Dis.76 (1995), 529–533. doi : PMID :8593374.  URI10.1016/0962-8479(95)90529-4
  12. M.A. Mori, G. Leonardson, T.K. Welty. The benefits of isoniazid chemoprophylaxis and risk factors for tuberculosis among Oglala Sioux Indians. Arch. Intern. Med.152 (1992), 547–50, doi : PMID :1546917  URI10.1001/archinte.152.3.547
  13. F. Mugusi, A.B. Swai, K.G. Alberti, D.G. McLarty. Increased prevalence of diabetes mellitus in patients with pulmonary tuberculosis in Tanzania. Tubercle71 (1990), 271–276, doi : PMID :2267680  URI10.1016/0041-3879(90)90040-F
  14. A. Pablos-Mèndez, J. Blustein, C.A. Knirsch. The role of diabetes mellitus in the higher prevalence of tuberculosis among Hispanics. Am J Public Health87 (1997), 574–579, doi : PMID :9146434  URI10.2105/AJPH.87.4.574
  15. C.Y. Jeon, M.B. Murray. Diabetes mellitus increases the risk of active tuberculosis : a systematic review of 13 observational studies. PLoS Med5 (2008), 152. doi : PMID :18630984  URI10.1371/journal.pmed.0050152
  16. I.B. Restrepo, A.J. Camerlin, M.H. Rahbar, W. Wang, M.A. Restrepo, I. Zarate, F. Mora-Guzmán, J. G. Crespo-Solis, J. Briggs, J. B. McCormicka, S. P. Fisher-Hocha. Cross-sectional assessment reveals high diabetes prevalence among newly-diagnosed tuberculosis cases. Bull. World Health. Organ.89 (2011), 352–359, doi : .  URI10.2471/BLT.10.085738 359
  17. M.M. McMahon, R.B. Bistrian. Host defenses and susceptibility to infection in patients with diabetes mellitus. Infect. Dis. Clin. North Am.9 (1995), 1-10.  
  18. H. Koziel, M.J. Koziel. Pulmonary complications of diabetes mellitus. Infect. Dis. Clin. North Am.9 (1995), 67–72.  
  19. K. Tsukaguchi, H. Okamura, M. Ikuno. The relation between diabetes mellitus and IFN-gamma, IL-12 and IL-IO production by CD4+ T cells and monocytcs in patients with pulmonary tuberculosis. Kekkaku, 72 (1997), 617–628.  
  20. M.A. Karuchunskn, V. Gcrgcrt, O.B. Lakovlcva. Specific features of cellular immunity of pulmonary tuberculosis in patients with diabetes mellitus. Problem Tnberk, 6 (1997), 59–63.  
  21. C.T. Yu, C.H. Wang, T.J. Huang. Relation of bronchoalvcolar lavagc T lymphocyte subpopulations to rate of regression of active pulmonary tuberculosis. Thorux50 (1995), 86–93.  
  22. A. Guptan, A. Shah. Tuberculosis and diabetes : An appraisa. Ind. J. Tub.47 (2000), 3–12.  
  23. C.R. Stevenson, N.G. Forouhi, G.C. Rogli, B.G. Williams, J.A. Lauer, C. Dye, N. Unwin. Diabetes and tuberculosis : the impact of the diabetes epidemic on tuberculosis incidence. BMC Public Health7 (2007), 234-242, doi :.  URI10.1186/1471-2458-7-234
  24. M.B. Murray, C.Y. Jeon. Diabetes mellitus increases the risk of active tuberculosis : A systematic review of 13 observational studies. PLoS Medicine5 (2008), 7–15, e152.doi :.  URI10.1371/journal.pmed.0050152
  25. C. Dye, B. Bourdin Trunz, K Lönnroth, G. Roglic, B.G. Williams. Nutrition, diabetes and tuberculosis in the epidemiological transition. PLoS One, 6(6) : e21161., 2011, doi :  URI10.1371/journal.pone.0021161
  26. K.E. Dooley, R.E. Chaisson. Tuberculosis and diabetes mellitus : convergence of two epidemics. Lancet Infect. Dis.9 (2009), 737–46.  
  27. C. Castillo-Chavez, B. Song. Dynamical models of tuberculosis and their applications. Math. Biosci. Eng.1 (2004), 361–404.  
  28. C.P. Bhunu, W. Garira, Z. Mukandavire, M. Zimba. Tuberculosis transmission model with chemoprophylaxis and treatment. Bull. Math. Biol.70 (2008), 1163–1191.  
  29. T. Cohen, C. Colijn, B. Finklea, M. Murray. Exogenous re-infection and the dynamics of tuberculosis epidemics : local effects in a network model of transmission. J. R. Soc. Interface4 (2007), 523–531.  
  30. S. Bowong, J.J. Tewa. Mathematical analysis of a tuberculosis model with differential infectivity. Com. Nonl. Sci. Num. Sim.14 (2009), 4010–4021.  
  31. Z. Feng, C.C. Chavez, A. F. Capurro. A model for tuberculosis with exogenous reinfection. Theor. Popul. Biol.57 (2000), 235–247.  
  32. B.M. Murphy, B.H. Singer, S. Anderson, S. Kirschner. Comparing epidemic tuberculosis in demographically distinct heterogeneous populations. Math. Biosci.180 (2002), 161–185.  
  33. R.W. Shafer, S.P. Singh, C. Larkin, P.M. Small. Exogenous reinfection with multidrug-resistant Mycobacterium tuberculosis in an immunocompetent patient. Tuberc. Lung Dis.76 (1995), 575–577.  
  34. K. Styblo, J. Meijer, I. Sutherland. The transmission of tubercle bacilli : its trend in a human population. Bull. Int. Union Tuberc.42 (1969), 5–104.  
  35. National Institute of Statistics, Evolution des systèmes statistiques nationaux, expérience du Cameroun, in The National Institute of Statistics report, J. Tedou (ed). New-York, (2010), 1–18.  
  36. National Comittee of Fight Against Tuberculosis, Guide du personnel de la santé, in The Ministry of Public Health report, Ministére de la Santé Publique (ed), Yaoundé-Cameroon : CEPER Press (2010), 1–110.  
  37. N. Bacaër, R. Ouifki, C. Pretorius, R. Wood, B. Williams. Modeling the joint epidemics of TB and HIV in a South African township. J. Math. Biol.57 (2008), 557–593, DOI .  URI10.1007/s00285-008-0177-z
  38. C. Dye, B.G. William. Criteria for the control of drug resistant tuberculosis. Proc. Natl. Acad. Sci. USA97 (2000), 8180–8185.  
  39. T. Cohen, M. Murray, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness, Nature Publishing Group,, (2004).  URIhttp://www.nature.com/naturemedicine
  40. G. Birkhoff, G.C. Rota, Ordinary Differential Equations. 4th edition, John Wiley and Sons, Inc., New York., 1989.  
  41. A. Berman, R.J. Plemmons, Nonnegative matrices in the mathematical sciences, SIAM., 1994.  
  42. J.A. Jacquez, C.P. Simon. Qualitative theory of compartmental systems. SIAM Rev.35 (1993), 43–79.  
  43. P. van den Driessche, J. Watmough. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Bios.180 (2002), 29–28.  
  44. C. Castillo-Chavez, Z. Feng, D. Xu, On the computation of ℛ0 and its role on global stability. math.la.asu.edu/chavez/2002/JB276.pdf, 2002.  
  45. J. Carr, Applications Centre Manifold theory. Springer-Verlag, New York, 1981.  
  46. O. Sharomi, A.B. Gumel. Curtailing smoking dynamics : a mathematical modeling approach. Appl. Math. Comput.19 (2008), 475–499.  
  47. N. Chitnis, J.M. Hyman, J.M. Cushing. Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull. Math. Biol.70 (2008), 1272–1296.  
  48. C.R. Stevenson, J.A. Critchley, N.G. Forouhi, G. Roglic, B.G. Williams. Diabetes and the risk of tuberculosis : a neglected threat to public health ?Chronic Illness3 (2007), 228–245,  
  49. C.K.W. Gavin Koh, W.J. Wiersinga. Tuberculosis and Diabetes Mellitus : Convergence of Two Epidemics : F1000 Ranking : “Changes Clinical Behavior”. Lancet Infect. Dis.9 (2009), 737–46.  
  50. C. Dye, B.B. Trunz, K. Lonnroth, G. Roglic, B.G. Williams. Nutrition, Diabetes and Tuberculosis in the Epidemiological Transition. PLoS ONE6(6) : e21161. doi :.  URI10.1371/journal.pone.0021161

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