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For the study of the dynamics of scabies in the population, the mathematical model is designed with delay differential equations (DDEs) for four subpopulations: unvaccinated individuals, vaccinated individuals, infected individuals, and recovered individuals. The fundamental properties of the model, such as positivity, boundedness, existence, and uniqueness, are proved. The equilibria, reproduction number, sensitivity analysis, and (Local and Global) stabilities for the second order are studied rigorously. The numerical simulations were performed to confirm the validity of their theoretical results. 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