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Item Open Access Mathematical modeling of infectious diseases and the impact of vaccination strategies(Mathematical Biosciences and Engineering, 2024) Bolatova D.; Kadyrov Sh.; Kashkynbayev A.Mathematical modeling plays a crucial role in understanding and combating infectious diseases, offering predictive insights into disease spread and the impact of vaccination strategies. This paper explored the significance of mathematical modeling in epidemic control efforts, focusing on the interplay between vaccination strategies, disease transmission rates, and population immunity. To facilitate meaningful comparisons of vaccination strategies, we maintained a consistent framework by fixing the vaccination capacity to vary from 10 to 100% of the total population. As an example, at a 50% vaccination capacity, the pulse strategy averted approximately 45.61% of deaths, while continuous and hybrid strategies averted around 45.18 and 45.69%, respectively. Sensitivity analysis further indicated that continuous vaccination has a more direct impact on reducing the basic reproduction number R0 compared to pulse vaccination. By analyzing key parameters such as R0 , pulse vaccination coefficients, and continuous vaccination parameters, the study underscores the value of mathematical modeling in shaping public health policies and guiding decision-making during disease outbreaksItem Open Access Mathematical Modelling of Hydrodynamics Problems by the Method of Fictitious Domains(Suleyman Demirel University, 2012) Kuttykozhaeva Sh. N.This paper investigates the method of fictitious domains for solving boundary value problems in hydrodynamics, extending its application to nonlinear elliptic equations. A rigorous justification of the method is presented, and a new approach to achieve the best possible convergence rate from the auxiliary problem to the original problem is proposed. The study demonstrates that as the small parameter tends to zero, the solution of the fictitious domain problem converges to the generalized solution of the original boundary value problem. The theoretical results include existence, uniqueness, and stability estimates, providing a solid mathematical foundation for applying the fictitious domain method in hydrodynamic modeling.