Math. Model. Nat. Phenom.
Volume 7, Number 3, 2012Epidemiology
|Page(s)||117 - 146|
|Published online||06 June 2012|
Analysis of The Impact of Diabetes on The Dynamical Transmission of Tuberculosis
Department of Mathematics, Faculty of Science, University of
Yaounde I, PO Box
2 Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon
3 Department of Mathematics and Physics, National Advanced School of Engineering (Polytechnic), University of Yaounde I, PO Box 8390 Yaounde, Cameroon
4 UMI 209 IRD/UPMC UMMISCO, Bondy-France and Project GRIMCAPE, LIRIMA, University of Yaounde I, Cameroon
5 The Abdus Salam International Centre for Theoretical Physics, PO Box 538, Strada Costiera 11 I-34014 Trieste, Italy
⋆ Corresponding author. E-mail: firstname.lastname@example.org
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.
Mathematics Subject Classification: 34A34 / 34D23 / 34D40 / 92D30
Key words: nonlinear dynamical systems / epidemiological models / diabetes / tuberculosis / stability / bifurcation
© EDP Sciences, 2012
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