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Mathematical modeling and dynamics of tuberculosis infection among diabetic patients in India


Diabetes is chronic, noncommunicable disease, affecting a large population, specially in asian countries like India and China. Tuberculosis is also a major threat to health worldwide. It has been reported that diabetes increases the risk of tuberculosis infection threefold and thus creating a joint epidemic. Therefore, in this article, we study the association of diabetes with tuberculosis infection through a Mathematical modeling approach. We have taken published data of diabetic people having tuberculosis infections from six DM clinics of Indian territory hospitals. For parameters, we have taken previously standarized published values. We have expressed the model with the help of differential equations. Further, we study the stability of the critical points for diabetes with tuberculosis infection. Finally, we perform some numerical experiments using fourth order Adams–Bashforth–Moulton predictor corrector method to improve some existing results. This study highlights that tuberculosis infections among diabetic people are higher. It also shows the pattern of tuberculosis infection among diabetic people. By finding stable point of these diseases outbreak, it gives us the insight about the preventive measures to control this joint epidemic in a better way.

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The authors would like to thank Department of Science and Technology DST-FIST Level-1 Program Grant No. SR/FST/MSI-092/2013 for providing the computational facilities. The third author was partially supported by a Grant from the Department of Science and Technology (DST-SERB), India under Grant No. EMR/2016/002883. The authors thank the anonymous reviewers for their valuable comments and helpful suggestions.

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Correspondence to Merina Dhara.

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Dhara, M., Baths, V. & Danumjaya, P. Mathematical modeling and dynamics of tuberculosis infection among diabetic patients in India. J Anal 27, 451–463 (2019).

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  • Diabetes mellitus (DM)
  • Tuberculosis (TB)
  • Population model
  • Joint epidemic
  • Stability of the critical points
  • Numerical experiments