Analyzing the Dynamic Characteristics of a Tuberculosis Epidemic Model Using Numerical Methods
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Abstract
Background: This study investigates the dynamic features of a viral model in tuberculosis using various numerical methods. The primary aim is to assess the performance of an analytical model for tuberculosis transmission using different numerical approaches and to compare the effectiveness of these methods in simulating the disease behavior under various conditions.
Methods: In this paper, the dynamics of tuberculosis are analyzed using the VSEIT epidemiological model and the numerical method NSFD. This model describes the community with five primary indicators: Vaccinated (V), Susceptible (S), Exposed (E), Infected (I), and Treatment (T) populations. The results indicate that the Non-Standard Finite Difference (NSFD) method is not only effective in accurately measuring the dynamic characteristics of the proposed model but also confirms the local and global stability of disease equilibrium.
Results: Simulation results demonstrate that the NSFD method is a unique and effective approach for controlling and predicting the spread of tuberculosis. This comparison underscores the effectiveness of this method compared to traditional Euler and fourth-order Runge-Kutta (RK4) methods.
Conclusion: This research contributes to a better understanding of tuberculosis epidemiology and offers potential control strategies for public health risks. The importance and effectiveness of the NSFD method in modeling the dynamic nature of tuberculosis are clearly highlighted. This study serves as a valuable recommendation in the field of controlling and predicting the spread of tuberculosis.
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