Browsing by Author "Bolatova D."

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    Mathematical modeling of infectious diseases and impact of vaccination
    (Faculty of Engineering and Natural Sciences, 2023) Bolatova D.
    The world is changing and evolving these days, and the various germs and viruses that surround us are also changing and evolving. For this reason, it is essential to choose the best strategy for combating these infections while preserving the health as much as possible. This coursework uses a fundamental mathematical term in bio-mathematics which is a basic reproduction number R0. It is a significant epidemiological term illustrating the number of infected people by one sick individual, hence giving the idea of a possible epidemics. Another thing to investigate in this coursework is a numerical approximation of the epidemic model under various scenarios to examine the model from a mathematical perspective. The following project covers the following topics: vaccination strategy, stability theory, mathematical biology, modeling of epidemics, optimization problems, and Python simulation. According to the epidemic model, one of the best strategies for immunizing the populace is pulse vaccination. The Next Generation matrix approach and the Hartman-Grobman method are two linearization techniques.
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    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 outbreaks