Geodesic
Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis
D.P. Moualeu1, 2 ; S. Bowong3, 2, 4 ; J.J. Tewa5, 2 ; Y. Emvudu1
1 Department of Mathematics, Faculty of Science, University of Yaounde I, PO Box 812 Yaounde, Cameroon
2 UMI 209 IRD/UPMC UMMISCO, Bondy-France and Project GRIMCAPE, LIRIMA, University of Yaounde I, Cameroon
3 Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon
4 The Abdus Salam International Centre for Theoretical Physics, PO Box 538, Strada Costiera 11 I-34014 Trieste, Italy
5 Department of Mathematics and Physics, National Advanced School of Engineering (Polytechnic), University of Yaounde I, PO Box 8390 Yaounde, Cameroon
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 3, pp. 117-146.

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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.
DOI : 10.1051/mmnp/20127309

D.P. Moualeu 1, 2 ; S. Bowong 3, 2, 4 ; J.J. Tewa 5, 2 ; Y. Emvudu 1

1 Department of Mathematics, Faculty of Science, University of Yaounde I, PO Box 812 Yaounde, Cameroon
2 UMI 209 IRD/UPMC UMMISCO, Bondy-France and Project GRIMCAPE, LIRIMA, University of Yaounde I, Cameroon
3 Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon
4 The Abdus Salam International Centre for Theoretical Physics, PO Box 538, Strada Costiera 11 I-34014 Trieste, Italy
5 Department of Mathematics and Physics, National Advanced School of Engineering (Polytechnic), University of Yaounde I, PO Box 8390 Yaounde, Cameroon 
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D.P. Moualeu; S. Bowong; J.J. Tewa; Y. Emvudu. Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 3, pp. 117-146. doi : 10.1051/mmnp/20127309. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20127309/

[1]

[2] C. Dye, B.G. Williams Science 2010 856 861

[3] K. Lönnroth, K.G. Castro, J.M. Chakaya, L.S. Chauhan, K. Floyd Lancet 2010 1814 1829

[4] J. Stephenson JAMA 2008 1764 1771

[5] The World Health Report, Diabetes, Fact sheet N0 312, http://www.who.int/mediacentre/factsheets/fs312/en/, Jan. 2011.

[6] American Diabetes Association. Diagnosis and classification of diabetes mellitus. Diabetes Care 32 (2008), 62–67.

[7]

[8] C. Dye Lancet 2006 938 940

[9] P.N. Oscarsson, H. Silwer Acta Med. Scand. 1958 23 48

[10] H.F. Root N. Engl. J. Med. 1934 1 13

[11] S.J. Kim, Y.P. Hong, W.J. Lew, S.C. Yang, E.G. Lee Tuber. Lung Dis. 1995 529 533

[12] M.A. Mori, G. Leonardson, T.K. Welty Arch. Intern. Med. 1992 547 50

[13] F. Mugusi, A.B. Swai, K.G. Alberti, D.G. Mclarty Increased prevalence of diabetes mellitus in patients with pulmonary tuberculosis in Tanzania Tubercle 1990 271 276

[14] A. Pablos-Mèndez, J. Blustein, C.A. Knirsch Am J Public Health 1997 574 579

[15] C.Y. Jeon, M.B. Murray PLoS Med 2008 152

[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 Bull. World Health. Organ. 2011 352 359

[17] M.M. Mcmahon, R.B. Bistrian Infect. Dis. Clin. North Am. 1995 1 10

[18] H. Koziel, M.J. Koziel Infect. Dis. Clin. North Am. 1995 67 72

[19] K. Tsukaguchi, H. Okamura, M. Ikuno Kekkaku 1997 617 628

[20] M.A. Karuchunskn, V. Gcrgcrt, O.B. Lakovlcva Problem Tnberk 1997 59 63

[21] C.T. Yu, C.H. Wang, T.J. Huang Thorux 1995 86 93

[22] A. Guptan, A. Shah Ind. J. Tub. 2000 3 12

[23] C.R. Stevenson, N.G. Forouhi, G.C. Rogli, B.G. Williams, J.A. Lauer, C. Dye, N. Unwin BMC Public Health 2007 234 242

[24] M.B. Murray, C.Y. Jeon PLoS Medicine 2008 7 15

[25] C. Dye, B. Bourdin Trunz, K Lönnroth, G. Roglic, B.G. Williams PLoS One 2011

[26] K.E. Dooley, R.E. Chaisson Lancet Infect. Dis. 2009 737 46

[27] C. Castillo-Chavez, B. Song Math. Biosci. Eng. 2004 361 404

[28] C.P. Bhunu, W. Garira, Z. Mukandavire, M. Zimba Bull. Math. Biol. 2008 1163 1191

[29] T. Cohen, C. Colijn, B. Finklea, M. Murray J. R. Soc. Interface 2007 523 531

[30] S. Bowong, J.J. Tewa Com. Nonl. Sci. Num. Sim. 2009 4010 4021

[31] Z. Feng, C.C. Chavez, A. F. Capurro Theor. Popul. Biol. 2000 235 247

[32] B.M. Murphy, B.H. Singer, S. Anderson, S. Kirschner Math. Biosci. 2002 161 185

[33] R.W. Shafer, S.P. Singh, C. Larkin, P.M. Small Tuberc. Lung Dis. 1995 575 577

[34] K. Styblo, J. Meijer, I. Sutherland Bull. Int. Union Tuberc. 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 J. Math. Biol. 2008 557 593

[38] C. Dye, B.G. William Proc. Natl. Acad. Sci. USA 2000 8180 8185

[39] T. Cohen, M. Murray, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness, Nature Publishing Group,http://www.nature.com/naturemedicine, (2004).

[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 SIAM Rev. 1993 43 79

[43] P. Van Den Driessche, J. Watmough Math. Bios. 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 Appl. Math. Comput. 2008 475 499

[47] N. Chitnis, J.M. Hyman, J.M. Cushing Bull. Math. Biol. 2008 1272 1296

[48] C.R. Stevenson, J.A. Critchley, N.G. Forouhi, G. Roglic, B.G. Williams Chronic Illness 2007 228 245

[49] C.K.W. Gavin Koh, W.J. Wiersinga Lancet Infect. Dis. 2009 737 46

[50] C. Dye, B.B. Trunz, K. Lonnroth, G. Roglic, B.G. Williams PLoS ONE

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