An effective mathematical representation and numerical simulation for TB prevention | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 33, Issue 1, 2025, Pages 29-47 PDF (631.39 K) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/joems.2025.331474.1017 | ||
| Author | ||
| هاله Emad* | ||
| department of mathematics, faculty of science , minia university | ||
| 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. | ||
| Keywords | ||
| Non-linear mathematical model; Tuberculosis transmission; Public health interventions; Stability and Sensitivity analysis; SCSC Technique | ||
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