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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: [email protected]
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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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