analyzing the dynamic characteristics of a tuberculosis epidemic model using numerical methods

Introduction: this study aims 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 disease behavior under various conditions. methods: this paper analyzes the dynamics of tuberculosis using the vseit epidemiological model and the numerical method nsfd (non-standard finite difference). the vseit model describes the community in terms of five key populations: vaccinated (v), susceptible (s), exposed (e), infected (i), and treated (t). the results demonstrate that the nsfd method is effective in accurately capturing the dynamic characteristics of the proposed model and also confirms the local and global stability of the 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: the importance and effectiveness of the nsfd method in modeling the dynamic nature of tuberculosis are highlighted. this study is a valuable recommendation for policymakers and public health officials by providing concrete insights into the control and prediction of tuberculosis spread, thereby enhancing the efficacy of intervention strategies.