An effective mathematical representation and numerical simulation for TB prevention

Document Type : Original Article

Author

department of mathematics, faculty of science , minia university

10.21608/joems.2025.331474.1017

Abstract

The primary motivation of this research is to develop a realistic non-linear mathematical
model that accurately represents the transmission dynamics of tuberculosis (TB). Unlike existing models, this study incorporates a comprehensive analysis of key preventive measures, such
as early detection, immunity, and personal hygiene, in mitigating the spread of TB bacteria.
By explicitly modeling the impact of these factors. In
addition, we aim with this study to develop a strategy to stop the spread of TB. The Shifted
Chebyshev Spectral Collocation Technique (SCSC) has been used to obtain numerical results.
The results obtained using the previously mentioned method show that as the immunity of community members improves, the number of recovered cases increases and the number of infected
cases decreases. The results also made clear the importance of detecting the disease at the
beginning of infection in order to prevent it and prevent the spread of infection, because the
timing of diagnosis TB affects the speed of recovery and limits the spread of infection. The
planned model consists of six epidemiological compartments. For the model, two steady-state
points have been determined, one with and one without the pandemic. An endemic point EE
is one that is present both locally and globally stable if R0 > 1. The stability shows that the
bacteria-free equilibrium (FE) is asymptotically stable both locally and globally for R0 < 1.
The model’s sensitivity is assessed. We can apply such a mathematical model to many other
infectious diseases.

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