Mathematical analysis of a two-strain tuberculosis model in Bangladesh

Kuddus, Md Abdul, McBryde, Emma S., Adekunle, Adeshina I., White, Lisa J., and Meehan, Michael T. (2022) Mathematical analysis of a two-strain tuberculosis model in Bangladesh. Scientific Reports, 12. 3634.

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Abstract

Tuberculosis (TB) is an airborne infectious disease that causes millions of deaths worldwide each year (1.2 million people died in 2019). Alarmingly, several strains of the causative agent, Mycobacterium tuberculosis (MTB)—including drug-susceptible (DS) and drug-resistant (DR) variants—already circulate throughout most developing and developed countries, particularly in Bangladesh, with totally drug-resistant strains starting to emerge. In this study we develop a two-strain DS and DR TB transmission model and perform an analysis of the system properties and solutions. Both analytical and numerical results show that the prevalence of drug-resistant infection increases with an increasing drug use through amplification. Both analytic results and numerical simulations suggest that if the basic reproduction numbers of both DS (R0s) and DR (R0r) TB are less than one, i.e. max[R0s, R0r]<1, the disease-free equilibrium is asymptotically stable, meaning that the disease naturally dies out. Furthermore, if R0r>max[R0s,1], then DS TB dies out but DR TB persists in the population, and if R0s>max[R0r,1] both DS TB and DR TB persist in the population. Further, sensitivity analysis of the model parameters found that the transmission rate of both strains had the greatest influence on DS and DR TB prevalence. We also investigated the effect of treatment rates and amplification on both DS and DR TB prevalence; results indicate that inadequate or inappropriate treatment makes co-existence more likely and increases the relative abundance of DR TB infections.

Item ID: 74404
Item Type: Article (Research - C1)
ISSN: 2045-2322
Copyright Information: © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Date Deposited: 14 Jun 2022 05:39
FoR Codes: 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490102 Biological mathematics @ 30%
42 HEALTH SCIENCES > 4202 Epidemiology > 420205 Epidemiological modelling @ 70%
SEO Codes: 20 HEALTH > 2004 Public health (excl. specific population health) > 200404 Disease distribution and transmission (incl. surveillance and response) @ 80%
20 HEALTH > 2002 Evaluation of health and support services > 200205 Health policy evaluation @ 20%
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