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Analysis of The Impact of Diabetes on The DynamicalTransmission of Tuberculosis

Published online by Cambridge University Press:  06 June 2012

D.P. Moualeu ,
S. Bowong ,
J.J. Tewa  and
Y. Emvudu
D.P. Moualeu
Affiliation:
Department of Mathematics, Faculty of Science, University of Yaounde I, PO Box 812 Yaounde, Cameroon UMI 209 IRD/UPMC UMMISCO, Bondy-France and Project GRIMCAPE, LIRIMA, University of Yaounde I, Cameroon
S. Bowong*
Affiliation:
Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon UMI 209 IRD/UPMC UMMISCO, Bondy-France and Project GRIMCAPE, LIRIMA, University of Yaounde I, Cameroon The Abdus Salam International Centre for Theoretical Physics, PO Box 538, Strada Costiera 11 I-34014 Trieste, Italy
J.J. Tewa
Affiliation:
Department of Mathematics and Physics, National Advanced School of Engineering (Polytechnic), University of Yaounde I, PO Box 8390 Yaounde, Cameroon UMI 209 IRD/UPMC UMMISCO, Bondy-France and Project GRIMCAPE, LIRIMA, University of Yaounde I, Cameroon
Y. Emvudu
Affiliation:
Department of Mathematics, Faculty of Science, University of Yaounde I, PO Box 812 Yaounde, Cameroon
*
⋆ Corresponding author. E-mail: sbowong@gmail.com
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Abstract

Tuberculosis (TB) remains a major global health problem. A possible risk factor for TB isdiabetes (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 aimedto assess the strength of the association between TB and DM. We present a deterministicmodel for TB in a community in order to determine the impact of DM in the spread of thedisease. The important mathematical features of the TB model are thoroughly investigated.The epidemic threshold known as the basic reproduction number and equilibria for the modelare determined and stabilities analyzed. The model is numerically analyzed to assess theimpact of DM on the transmission dynamics of TB. We perform sensitivity analysis on thekey parameters that drive the disease dynamics in order to determine their relativeimportance to disease transmission and prevalence. Numerical simulations suggest that DMenhances the TB transmission and progression to active TB in a community. The resultssuggest that there is a need for increased attention to intervention strategies such asthe chemoprophylaxis of TB latent individuals and treatment of active TB in people withDM, which may include testing for suspected diabetes, improved glucose control, andincreased clinical and therapeutic monitoring in order to reduce the burden of thedisease.

Keywords

nonlinear dynamical systemsepidemiological modelsdiabetestuberculosisstabilitybifurcation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 3: Epidemiology , 2012 , pp. 117 - 146
Copyright
© EDP Sciences, 2012

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References

Global tuberculosis report. Geneva : World Health Organization ; Available from : http://whqlibdoc.who.int/publications/2010/9789241564069-eng.pdf [accessed 25 March 2011], 2010.
Dye, C., Williams, B.G.. The population dynamics and control of tuberculosis. Science 328 (2010), 856–861. CrossRefGoogle Scholar
Lönnroth, K., Castro, K.G., Chakaya, J.M., Chauhan, L.S., Floyd, K.. Tuberculosis control and elimination 2010–50 : cure, care, and social development. Lancet 375 (2010), 1814-1829. CrossRefGoogle ScholarPubMed
Stephenson, J.. TB progress slowing. JAMA 299 (2008), 1764-1771, doi : 10.1001/jama.299.15.1764-b. Google Scholar
The World Health Report, Diabetes, Fact sheet N 0 312, http://www.who.int/mediacentre/factsheets/fs312/en/, Jan. 2011.
American Diabetes Association. Diagnosis and classification of diabetes mellitus. Diabetes Care 32 (2008), 62–67.
Diabetes atlas. Brussels, International Diabetes Federation ; Available from : http://www.diabetesatlas.org/ 2010, [accessed 25 March 2011].
Dye, C.. Global epidemiology of tuberculosis. Lancet 367 (2006), 938–940, doi :10.1016/S0140-6736(06)68384-0 PMID :16546542. CrossRefGoogle Scholar
Oscarsson, P.N., Silwer, H.. Incidence of pulmonary tuberculosis among diabetics. Acta Med. Scand. 335 (1958), 23–48. Google Scholar
Root, H.F.. The association of diabetes and tuberculosis. N. Engl. J. Med. 210 (1934), 1–13. doi :10.1056/NEJM193401042100101. CrossRefGoogle Scholar
Kim, S.J., Hong, Y.P., Lew, W.J., Yang, S.C., Lee, E.G.. Incidence of pulmonary tuberculosis among diabetics. Tuber. Lung Dis. 76 (1995), 529–533. doi :10.1016/0962-8479(95)90529-4 PMID :8593374. CrossRefGoogle ScholarPubMed
Mori, M.A., Leonardson, G., Welty, T.K.. The benefits of isoniazid chemoprophylaxis and risk factors for tuberculosis among Oglala Sioux Indians. Arch. Intern. Med. 152 (1992), 547–50, doi :10.1001/archinte.152.3.547 PMID :1546917 CrossRefGoogle ScholarPubMed
Mugusi, F., Swai, A.B., Alberti, K.G., McLarty, D.G.. Increased prevalence of diabetes mellitus in patients with pulmonary tuberculosis in Tanzania. Tubercle 71 (1990), 271–276, doi :10.1016/0041-3879(90)90040-F PMID :2267680 CrossRefGoogle Scholar
Pablos-Mèndez, A., Blustein, J., Knirsch, C.A.. The role of diabetes mellitus in the higher prevalence of tuberculosis among Hispanics. Am J Public Health 87 (1997), 574–579, doi :10.2105/AJPH.87.4.574 PMID :9146434 CrossRefGoogle ScholarPubMed
Jeon, C.Y., Murray, M.B.. Diabetes mellitus increases the risk of active tuberculosis : a systematic review of 13 observational studies. PLoS Med 5 (2008), 152. doi :10.1371/journal.pmed.0050152 PMID :18630984 CrossRefGoogle ScholarPubMed
Restrepo, I.B., Camerlin, A.J., Rahbar, M.H., Wang, W., Restrepo, M.A., Zarate, I., Mora-Guzmán, F., Crespo-Solis, J. G., Briggs, J., McCormicka, J. B., Fisher-Hocha, S. P.. Cross-sectional assessment reveals high diabetes prevalence among newly-diagnosed tuberculosis cases. Bull. World Health. Organ. 89 (2011), 352–359, doi :10.2471/BLT.10.085738 359 . CrossRefGoogle Scholar
McMahon, M.M., Bistrian, R.B.. Host defenses and susceptibility to infection in patients with diabetes mellitus. Infect. Dis. Clin. North Am. 9 (1995), 1-10. Google ScholarPubMed
Koziel, H., Koziel, M.J.. Pulmonary complications of diabetes mellitus. Infect. Dis. Clin. North Am. 9 (1995), 67–72. Google ScholarPubMed
Tsukaguchi, K., Okamura, H., Ikuno, M.. 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. Google Scholar
Karuchunskn, M.A., Gcrgcrt, V., Lakovlcva, O.B.. Specific features of cellular immunity of pulmonary tuberculosis in patients with diabetes mellitus. Problem Tnberk, 6 (1997), 59–63. Google Scholar
Yu, C.T., Wang, C.H., Huang, T.J.. Relation of bronchoalvcolar lavagc T lymphocyte subpopulations to rate of regression of active pulmonary tuberculosis. Thorux 50 (1995), 86–93. Google ScholarPubMed
Guptan, A., Shah, A.. Tuberculosis and diabetes : An appraisa. Ind. J. Tub. 47 (2000), 3–12. Google Scholar
Stevenson, C.R., Forouhi, N.G., Rogli, G.C., Williams, B.G., Lauer, J.A., Dye, C., Unwin, N.. Diabetes and tuberculosis : the impact of the diabetes epidemic on tuberculosis incidence. BMC Public Health 7 (2007), 234-242, doi :10.1186/1471-2458-7-234. CrossRefGoogle Scholar
Murray, M.B., Jeon, C.Y.. Diabetes mellitus increases the risk of active tuberculosis : A systematic review of 13 observational studies. PLoS Medicine 5 (2008), 7–15, e152.doi :10.1371/journal.pmed.0050152. Google Scholar
Dye, C., Bourdin Trunz, B., Lönnroth, K, Roglic, G., Williams, B.G.. Nutrition, diabetes and tuberculosis in the epidemiological transition. PLoS One, 6(6) : e21161., 2011, doi : 10.1371/journal.pone.0021161 CrossRefGoogle Scholar
Dooley, K.E., Chaisson, R.E.. Tuberculosis and diabetes mellitus : convergence of two epidemics. Lancet Infect. Dis. 9 (2009), 737–46. CrossRefGoogle ScholarPubMed
Castillo-Chavez, C., Song, B.. Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 1 (2004), 361–404. CrossRefGoogle ScholarPubMed
Bhunu, C.P., Garira, W., Mukandavire, Z., Zimba, M.. Tuberculosis transmission model with chemoprophylaxis and treatment. Bull. Math. Biol. 70 (2008), 1163–1191. CrossRefGoogle ScholarPubMed
Cohen, T., Colijn, C., Finklea, B., Murray, M.. Exogenous re-infection and the dynamics of tuberculosis epidemics : local effects in a network model of transmission. J. R. Soc. Interface 4 (2007), 523–531. CrossRefGoogle Scholar
Bowong, S., Tewa, J.J.. Mathematical analysis of a tuberculosis model with differential infectivity. Com. Nonl. Sci. Num. Sim. 14 (2009), 4010–4021. CrossRefGoogle Scholar
Feng, Z., Chavez, C.C., Capurro, A. F.. A model for tuberculosis with exogenous reinfection. Theor. Popul. Biol. 57 (2000), 235–247. CrossRefGoogle ScholarPubMed
Murphy, B.M., Singer, B.H., Anderson, S., Kirschner, S.. Comparing epidemic tuberculosis in demographically distinct heterogeneous populations. Math. Biosci. 180 (2002), 161–185. CrossRefGoogle ScholarPubMed
Shafer, R.W., Singh, S.P., Larkin, C., Small, P.M.. Exogenous reinfection with multidrug-resistant Mycobacterium tuberculosis in an immunocompetent patient. Tuberc. Lung Dis. 76 (1995), 575–577. CrossRefGoogle Scholar
Styblo, K., Meijer, J., Sutherland, I.. The transmission of tubercle bacilli : its trend in a human population. Bull. Int. Union Tuberc. 42 (1969), 5–104. Google Scholar
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.
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.
Bacaër, N., Ouifki, R., Pretorius, C., Wood, R., Williams, B.. Modeling the joint epidemics of TB and HIV in a South African township. J. Math. Biol. 57 (2008), 557–593, DOI 10.1007/s00285-008-0177-z. CrossRefGoogle Scholar
Dye, C., William, B.G.. Criteria for the control of drug resistant tuberculosis. Proc. Natl. Acad. Sci. USA 97 (2000), 8180–8185. CrossRefGoogle ScholarPubMed
T. Cohen, M. Murray, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness, Nature Publishing Group,http://www.nature.com/naturemedicine, (2004).
G. Birkhoff, G.C. Rota, Ordinary Differential Equations. 4th edition, John Wiley and Sons, Inc., New York., 1989.
A. Berman, R.J. Plemmons, Nonnegative matrices in the mathematical sciences, SIAM., 1994.
Jacquez, J.A., Simon, C.P.. Qualitative theory of compartmental systems. SIAM Rev. 35 (1993), 43–79. CrossRefGoogle Scholar
van den Driessche, P., Watmough, J.. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Bios. 180 (2002), 29–28. CrossRefGoogle ScholarPubMed
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.
J. Carr, Applications Centre Manifold theory. Springer-Verlag, New York, 1981.
Sharomi, O., Gumel, A.B.. Curtailing smoking dynamics : a mathematical modeling approach. Appl. Math. Comput. 19 (2008), 475–499. Google Scholar
Chitnis, N., Hyman, J.M., Cushing, J.M.. Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull. Math. Biol. 70 (2008), 1272–1296. CrossRefGoogle Scholar
Stevenson, C.R., Critchley, J.A., Forouhi, N.G., Roglic, G., Williams, B.G.. Diabetes and the risk of tuberculosis : a neglected threat to public health ? Chronic Illness 3 (2007), 228–245, CrossRefGoogle Scholar
Gavin Koh, C.K.W., Wiersinga, W.J.. Tuberculosis and Diabetes Mellitus : Convergence of Two Epidemics : F1000 Ranking : “Changes Clinical Behavior”. Lancet Infect. Dis. 9 (2009), 737–46. Google Scholar
Dye, C., Trunz, B.B., Lonnroth, K., Roglic, G., Williams, B.G.. Nutrition, Diabetes and Tuberculosis in the Epidemiological Transition. PLoS ONE 6(6) : e21161. doi :10.1371/journal.pone.0021161. PubMed