Modeling the Transmission Dynamics of Tuberculosis and Predicting Its Prevalence in Bangladesh Using SEIR Framework

Abstract

Tuberculosis (TB) is one of the top ten most common infectious diseases in the world. It is also a serious public health problem in Bangladesh, with the number of patients increasing at an alarming rate. In this paper, we are interested in learning more about Bangladesh’s dynamics of tuberculosis, and for this purpose, we proposed and analyzed a four-compartmental model namely the SEIR model. According to the model, the disease-free equilibrium point is asymptotically stable (unstable), and the endemic equilibrium point is unstable (asymptotically stable) if the basic reproduction number is less than (greater than) unity. We analytically calculate the basic reproduction number, and based on the number, we perform the stability analysis of the model at the equilibrium points to understand the epidemic and endemic cases. In our model, the parameters play a significant role in controlling the spread of TB which are generated from TB-reported data from 2016 to 2021 in Bangladesh using the least squares method. The obtained results indicate that the basic reproduction number is greater than unity and this means that TB disease is increasing at an alarming rate every year, and the control strategies should be changed through an alternative system. Moreover, the stability analysis and the sensitivity analysis by numerical and graphical simulation of the model parameters are presented and discussed. The graphical solutions of the model equations were developed using MATLAB as well as computer simulations, and we calculated the model prediction and then compared it to the reported data. Finally, we discuss the accuracy and reliability of the model’s results.