Stability and sensitivity analysis of an infectious respiratory disease with vaccination and use of face masks
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Abstract
Mathematical modeling serves as a vital tool in public health, enabling policymakers to synthesize evidence, forecast disease trends, and assess intervention strategies. This study investigated the combined effects of face masks, quarantine, social distancing, and vaccination in controlling infectious respiratory diseases. The reproduction number was derived using the next-generation matrix (NGM). Local stability analysis utilized the Gershgorin Circle Theorem, while global stability was analyzed through the Quadratic Lyapunov Theorem. Sensitivity analysis was conducted using the normalized forward sensitivity index, and numerical simulations were performed with Python libraries such as \textit{scipy, numpy}, and \textit{matplotlib.pyplot}. Bifurcation analysis was carried out using the Center Manifold Theorem. The findings revealed that while these measures effectively reduced infection spread, they were insufficient to completely eliminate disease transmission. This study underscores the importance of implementing multiple strategies concurrently to effectively control the transmission of infectious diseases and guide public health interventions.
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