Mathematical modeling of infectious diseases and the impact of vaccination strategies

Diana Bolatova; Shirali Kadyrov; Ardak Kashkynbayev; Diana Bolatova; Shirali Kadyrov; Ardak Kashkynbayev

doi:10.3934/mbe.2024314

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 9: 7103-7123. doi: 10.3934/mbe.2024314

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Mathematical modeling of infectious diseases and the impact of vaccination strategies

1.
Department of Mathematics and Natural Sciences, SDU University, Kaskelen 040900, Kazakhstan
2.
General Education Department, New Uzbekistan University, Movarounnahr Street 1, Tashkent 100000, Uzbekistan
3.
Department of Mathematics, School of Sciences and Humanities, Nazarbayev University, Qabanbay Batyr Ave 53, Astana 010000, Kazakhstan

Received: 26 June 2024 Revised: 20 August 2024 Accepted: 06 September 2024 Published: 19 September 2024

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 $ R_0 $ compared to pulse vaccination. By analyzing key parameters such as $ R_0 $, 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.
- mathematical modeling,
- infectious diseases,
- vaccination strategies,
- epidemic control,
- disease transmission,
- dynamical systems,
- immunity,
- vaccine effectiveness,
- public health,
- epidemiology
Citation: Diana Bolatova, Shirali Kadyrov, Ardak Kashkynbayev. Mathematical modeling of infectious diseases and the impact of vaccination strategies[J]. Mathematical Biosciences and Engineering, 2024, 21(9): 7103-7123. doi: 10.3934/mbe.2024314

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Abstract

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 $ R_0 $ compared to pulse vaccination. By analyzing key parameters such as $ R_0 $, 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.

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