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

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

Affiliations:

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

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.

Keywords

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

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DOI

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

Citation (APA)

Rahman, S. M. S., Mondal, R., Santa, S., Anisujjaman, M., Ferdushi, K. F., & Haque, M. R. (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. https://doi.org/10.21833/ijaas.2025.12.020