Speaker
Description
Abstract
This study presents a six-compartment deterministic model for tuberculosis TB) transmission dynamics in populations stratified by comorbidity status. TB caused 1.3 million deaths globally in 2023, while diabetes(a major TB comorbidity), affects 537 million adults and contributes to $15-20\%$ of TB cases worldwide \cite{bi_comments_2025, kumar_prevalence_2024}. The syndemic is most severe in high-burden nations: India, Indonesia, China and the Philippines account for nearly half of the 10.8 million annual TB cases, with diabetes prevalence among TB patients exceeding $15\%$ globally reaching $>45\%$ in parts of the Western Pacific [\cite{kumar_prevalence_2024}]. The model includes elevated TB susceptibility in comorbid individuals ($\alpha_c\geq\alpha$), accelerated progression to active disease ($\delta_c\geq\delta$), increased mortality ($\nu_c\geq\nu$), reduced recovery ($\gamma_c\leq\gamma$), and comorbidity acquisition $\theta$. Cross-transmission between subpopulations occurs via weighted infectious pressure $T=\beta I+\beta _cI_c$. The Jacobian matrix is derived to enable equilibrium stability analysis; the basic reproduction number $\mathcal{R}_0$ is computed, and critical parameters driving TB persistence are identified. Numerical simulations show that rising comorbidity prevalence substantially increase endemic TB burden, risking elimination goals.
Keywords: Tuberculosis; Comorbidity; Mathematical modeling;Stability analysis; $\mathcal{R}_0$
Bibliography
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title = {The construction of next-generation matrices for compartmental epidemic models},
volume = {7},
issn = {1742-5689, 1742-5662},
url = {https://royalsocietypublishing.org/doi/10.1098/rsif.2009.0386},
doi = {10.1098/rsif.2009.0386},
abstract = {The basic reproduction number ℛ
0
is arguably the most important quantity in infectious disease epidemiology. The next-generation matrix (NGM) is the natural basis for the definition and calculation of ℛ
0
where finitely many different categories of individuals are recognized. We clear up confusion that has been around in the literature concerning the construction of this matrix, specifically for the most frequently used so-called compartmental models. We present a detailed easy recipe for the construction of the NGM from basic ingredients derived directly from the specifications of the model. We show that two related matrices exist which we define to be the
NGM with large domain
and the
NGM with small domain
. The three matrices together reflect the range of possibilities encountered in the literature for the characterization of ℛ
0
. We show how they are connected and how their construction follows from the basic model ingredients, and establish that they have the same non-zero eigenvalues, the largest of which is the basic reproduction number ℛ
0
. Although we present formal recipes based on linear algebra, we encourage the construction of the NGM by way of direct epidemiological reasoning, using the clear interpretation of the elements of the NGM and of the model ingredients. We present a selection of examples as a practical guide to our methods. In the appendix we present an elementary but complete proof that ℛ
0
defined as the dominant eigenvalue of the NGM for compartmental systems and the Malthusian parameter
r
, the real-time exponential growth rate in the early phase of an outbreak, are connected by the properties that ℛ
0
{\textgreater} 1 if and only if
r
{\textgreater} 0, and ℛ
0
= 1 if and only if
r
= 0.},
language = {en},
number = {47},
urldate = {2026-03-13},
journal = {Journal of The Royal Society Interface},
author = {Diekmann, O. and Heesterbeek, J. A. P. and Roberts, M. G.},
month = jun,
year = {2010},
pages = {873--885},
}
@article{bi_comments_2025,
title = {Comments on the {WHO} {Global} {Tuberculosis} {Report} 2024: {Progress}, {Challenges} and {Innovations} for {Achieving} {End} {TB} {Strategy} by 2035},
volume = {7},
issn = {2641-5917},
shorttitle = {Comments on the {WHO} {Global} {Tuberculosis} {Report} 2024},
url = {https://journals.lww.com/10.1097/IM9.0000000000000169},
doi = {10.1097/IM9.0000000000000169},
language = {en},
number = {1},
urldate = {2026-03-15},
journal = {Infectious Microbes and Diseases},
author = {Bi, Kefan and Zhao, Yanlin and Lu, Shuihua and Xu, Kaijin and Zhang, Ying},
month = mar,
year = {2025},
pages = {1--4},
}
@article{kumar_prevalence_2024,
title = {Prevalence of {Diabetes} in {India}: {A} {Review} of {IDF} {Diabetes} {Atlas} 10th {Edition}},
volume = {20},
issn = {15733998},
shorttitle = {Prevalence of {Diabetes} in {India}},
url = {https://www.eurekaselect.com/215752/article},
doi = {10.2174/1573399819666230413094200},
abstract = {Abstract:
Diabetes is a severe chronic disease that arises when insulin generation is insufficient, or
the generated insulin cannot be used in the body, resulting a long-term metabolic disorder. Diabetes
affects an estimated 537 million adults worldwide between the age of 20 to 79 (10.5\% of all
adults in this age range). By 2030, 643 million people will have diabetes globally, increasing to
783 million by 2045. According to the IDF 10th edition, the incidence of diabetes has been rising
in South-East Asia (SEA) nations for at least 20 years, and current estimates have outperformed all
previous forecasts. This review aims to provide updated estimates and future projections of diabetes
prevalence at the national and global levels by using data from the 10th edition of the IDF Diabetes
Atlas 2021. For this review, we studied more than 60 previously published related articles
from various sources, such as PubMed and Google Scholar, and we extracted 35 studies out of 60.
however, we used only 34 studies directly related to diabetes and its prevalence at the global, SEA,
and Indian levels. This review article concludes that in 2021 more than 1 in 10 adults worldwide
developed diabetes. The estimated prevalence of diabetes in adults (20 to 79 years) has more than
tripled since the first edition in 2000, rising from an estimated 151 million (4.6\% of the world’s
population at the time) to 537.5 million (10.5\%) of the world’s population today. The prevalence
rate will be higher than 12.8\% by 2045. In addition, this study indicates that the incidence of diabetes
in the world, Southeast Asia, and India was 10.5\%, 8.8\%, and 9.6\%, respectively, throughout
2021 and will rise to 12.5\%, 11.5\%, and 10.9\%, respectively by 2045.},
language = {en},
number = {1},
urldate = {2026-03-15},
journal = {Current Diabetes Reviews},
author = {Kumar, Arvind and Gangwar, Ruby and Ahmad Zargar, Abrar and Kumar, Ranjeet and Sharma, Amit},
month = jan,
year = {2024},
pages = {e130423215752},
}
@article{moualeu_analysis_2012,
title = {Analysis of {The} {Impact} of {Diabetes} on {The} {Dynamical} {Transmission} of {Tuberculosis}},
volume = {7},
issn = {0973-5348, 1760-6101},
url = {http://www.mmnp-journal.org/10.1051/mmnp/20127309},
doi = {10.1051/mmnp/20127309},
number = {3},
urldate = {2026-03-15},
journal = {Mathematical Modelling of Natural Phenomena},
author = {Moualeu, D.P. and Bowong, S. and Tewa, J.J. and Emvudu, Y.},
year = {2012},
pages = {117--146},
}
@article{malik_mathematical_2018,
title = {Mathematical modeling and numerical simulation of tuberculosis spread with diabetes effect},
volume = {1108},
copyright = {http://iopscience.iop.org/info/page/text-and-data-mining},
issn = {1742-6588, 1742-6596},
url = {https://iopscience.iop.org/article/10.1088/1742-6596/1108/1/012061},
doi = {10.1088/1742-6596/1108/1/012061},
urldate = {2026-03-15},
journal = {Journal of Physics: Conference Series},
author = {Malik, Maulana and Larasati, Monica and Aldila, Dipo},
month = nov,
year = {2018},
pages = {012061},
}
