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Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

机译:估算印度Covid-19传输动态的分数SIR模型

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In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model’s transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.
机译:在本文中,构建了一种时间依赖性敏感感染恢复(SIR)模型,以研究印度各个地区Covid-19的传输速率。该模型包括哪个基本参数,其中感染的透射率依赖于各个区域中的群体密度,接触率,回收率和感染强度。看着印度不同地理位置的巨大多样性,我们决心根据Covid-19数据计算所有印度地区的基本再生数,直到2020年7月7日。通过在ArcGIS的帮助下准备区域方面的空间分布图,该模型用于展示完全锁定对印度地区Covid-19感染的传输速率的影响。此外,通过模型对分数有序动态系统的转换,我们发现所提出的SIR模型的性质对于系统的不同顺序不同。基本再现数的敏感性分析是以图形方式进行的,这预测了Covid-19感染的传输速率变化与不同参数的变化。在数值模拟部分中,模型隔间中的振荡和变体显示为两个不同的情况,有和没有锁定。

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