Abstract
In this study, we develop and analyze a deterministic mathematical model for tuberculosis (TB) transmission dynamics. The model includes vaccination for newborns and treatment for both high-risk latent and active TB patients. The stability of disease-free equilibrium point is discussed in detail. In the numerical simulation, the model parameters are estimated using reported TB incidence data in Ethiopia from the years 2003 to 2017, and R0 is calculated as R0≈2.13. Finally, the sensitivity indices of R0 with respect to the model parameters are performed, and their corresponding graphical results are presented. Our results quantify the positive influence of vaccination and the treatment for high-risk latent and active TB patients on the control of tuberculosis.
Highlights
Tuberculosis (TB) is an airborne and highly infectious disease caused by Mycobacterium tuberculosis
We studied a tuberculosis transmission dynamics model with vaccination and treatment for both high-risk latent and active TB infected classes. e reproduction number is calculated and the equilibrium points are described
We showed that the disease-free equilibrium point
Summary
Tuberculosis (TB) is an airborne and highly infectious disease caused by Mycobacterium tuberculosis. According to the WHO report, Ethiopia is one of the 30 high-burden countries, and there were an estimated 172,000 (164 per 100,000 populations) incident cases of TB in 2017. For many years mathematical models have been applied to study the transmission dynamics of TB. Moualeu et al [15] developed a model for the transmission dynamics of TB and applied to the data for Cameroon. Eir result showed that applying a combination of distancing and case nding control strategies has signi cant potential for curtailing the spread of TB in the Philippines. Erefore the transmission dynamics of TB by mathematical models are important for proposing the best mechanisms to control the spread of TB. E purpose of this study is to develop a suitable TB dynamics model and calibrating it for Ethiopia Eir result showed that applying a combination of distancing and case nding control strategies has signi cant potential for curtailing the spread of TB in the Philippines. erefore the transmission dynamics of TB by mathematical models are important for proposing the best mechanisms to control the spread of TB. e purpose of this study is to develop a suitable TB dynamics model and calibrating it for Ethiopia
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