Mathematical modeling of infectious diseases and the impact of vaccination strategies

Bolatova D. Kadyrov S. Kashkynbayev A.
2024 American Institute of Mathematical Sciences

Mathematical Biosciences and Engineering
2024 #21 Issue 9 7103 - 7123 pp.

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.

disease transmission , dynamical systems , epidemic control , epidemiology , immunity , infectious diseases , mathematical modeling , public health , vaccination strategies , vaccine effectiveness

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Department of Mathematics and Natural Sciences, SDU University, Kaskelen, 040900, Kazakhstan
General Education Department, New Uzbekistan University, Movarounnahr Street 1, Tashkent, 100000, Uzbekistan
Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Qabanbay Batyr Ave 53, Astana, 010000, Kazakhstan

Department of Mathematics and Natural Sciences
General Education Department
Department of Mathematics

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