A New Mathematical Modeling of the COVID-19 Pandemic Including the Vaccination Campaign

M. Yavuz, Fatma Özlem Coşar, Fatma Günay, F. Özdemi̇r
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引用次数: 47

Abstract

In a short time, many illustrative studies have been conducted on the mathematical modeling and analysis of COVID-19. There are not enough studies taking into account the vaccine campaign among these studies. In this context, a mathematical model is developed to reveal the effects of vaccine treatment, which has been performed recently, on COVID-19 in this study. In the proposed model, as well as the vaccinated individuals, a five-dimensional compartment system including the susceptible, infected, exposed and recovered population is constructed. Moreover, besides the positivity, existence and uniqueness of the solution, biologically feasible region are provided. The basic reproduction number known as expected secondary infection which means that expected infection among the susceptible populations caused by this infection is evaluated. In the numerical simulations, the parameter values taken from the literature and estimated are used to perform the solutions of the proposed model. Fourth-order Runge-Kutta numerical scheme is applied to obtain the results.
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包括疫苗接种运动在内的新型COVID-19大流行数学模型
在短时间内,对新冠肺炎的数学建模和分析进行了许多说明性研究。在这些研究中,没有足够的研究考虑到疫苗运动。在此背景下,本研究开发了一个数学模型,以揭示最近进行的疫苗治疗对新冠肺炎的影响。在所提出的模型中,以及接种疫苗的个体,构建了一个包括易感人群、感染人群、暴露人群和康复人群的五维隔间系统。此外,除了解的正性、存在性和唯一性之外,还提供了生物学上可行的区域。被称为预期二次感染的基本繁殖数,这意味着对由这种感染引起的易感人群中的预期感染进行评估。在数值模拟中,使用从文献中获得的参数值和估计值来执行所提出的模型的求解。应用四阶龙格-库塔数值格式得到了结果。
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