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@article{192308,
        author = {Prof Ansari Naziya Abdul Kadir},
        title = {Stability and Bifurcation Analysis of an SIR Epidemic Model with Vaccination},
        journal = {International Journal of Innovative Research in Technology},
        year = {2026},
        volume = {12},
        number = {9},
        pages = {888-896},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=192308},
        abstract = {Mathematical modeling provides a powerful framework for understanding the spread of infectious diseases and evaluating control strategies. In this study, a susceptible–infected–recovered (SIR) epidemic model incorporating vaccination is proposed and analyzed. The model is formulated as a system of nonlinear ordinary differential equations. The basic reproduction number R_0is derived to characterize the threshold behavior of disease transmission. Stability analysis is performed to investigate the local and global dynamics of the equilibrium points. Bifurcation analysis is carried out to study qualitative changes in the system near critical parameter values. Sensitivity analysis is used to determine the relative importance of model parameters. Numerical simulations based on the fourth-order Runge–Kutta method are presented to validate the analytical results. The results demonstrate that vaccination significantly reduces the infected population and plays a crucial role in preventing epidemic outbreaks.},
        keywords = {SIR model; infectious disease; vaccination; stability analysis; bifurcation; sensitivity analysis; numerical simulation},
        month = {February},
        }