International Journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

Frequency: 12

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 Volume 12, Issue 12 (December 2025), Pages: 229-236

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 Original Research Paper

Mathematical analysis of the SEIRD model for the spread of tuberculosis in Bangladesh

 Author(s): 

 S. M. Saydur Rahman 1, Ritu Mondal 1, *, Sarmin Santa 1, Md. Anisujjaman 1, Kanis Fatama Ferdushi 2, Md. Rejwanul Haque 1

 Affiliation(s):

  1Department of Mathematics, Shahjalal University of Science and Technology, Sylhet, Bangladesh
  2Department of Statistics, Shahjalal University of Science and Technology, Sylhet, Bangladesh

 Full text

    Full Text - PDF

 * Corresponding Author. 

   Corresponding author's ORCID profile:  https://orcid.org/0009-0006-1871-138X

 Digital Object Identifier (DOI)

  https://doi.org/10.21833/ijaas.2025.12.020

 Abstract

The Susceptible-Infected-Recovered (SIR) model is a mathematical framework commonly used to understand how infectious diseases spread within a population. Building on this foundation, we examine an extended model known as the Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) model. This model is applied to study the spread of multidrug-resistant tuberculosis (MDR-TB), a critical and growing public health concern in Bangladesh. To evaluate the model, we use the basic reproduction number, which is calculated through the next-generation matrix method. The results indicate that when the reproduction number is below a certain threshold, the disease-free equilibrium is locally stable and the infection gradually disappears. However, if the reproduction number exceeds that threshold, the system's equilibrium points become locally asymptotically stable. In this study, we also carry out numerical simulations to assess the impact of MDR-TB in Bangladesh over the period from 2008 to 2020.

 © 2025 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords

 Tuberculosis modeling, Reproduction number, MDR-TB dynamics, SEIRD framework, Disease equilibrium

 Article history

 Received 29 January 2025, Received in revised form 6 June 2025, Accepted 29 November 2025

 Acknowledgment

Partial financial support for this research was provided by the SUST Research Center (Grant No. PS/2024/1/26). 

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Rahman SMS, Mondal R, Santa S, Anisujjaman M, Ferdushi KF, and Haque MR (2025). Mathematical analysis of the SEIRD model for the spread of tuberculosis in Bangladesh. International Journal of Advanced and Applied Sciences, 12(12): 229-236

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 Figures

  Fig. 1  Fig. 2  Fig. 3  Fig. 4  Fig. 5  Fig. 6  Fig. 7  Fig. 8  Fig. 9  Fig. 10 

 Tables

  Table 1  Table 2  Table 3  Table 4

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