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COVID-19 spreading: a recursive model

机译：Covid-19传播：递归模型

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Background The major medical and social challenge of the 21st century is COVID-19, caused by the novel coronavirus SARS-CoV-2. Critical issues include the rate at which the coronavirus spreads and the effect of quarantine measures and population vaccination on this rate. Knowledge of the laws of the spread of COVID-19 will enable assessment of the effectiveness and reasonableness of the quarantine measures used, as well as determination of the necessary level of vaccination needed to overcome this crisis. Objective This study aims to establish the laws of the spread of COVID-19 and to use them to develop a mathematical model to predict changes in the number of active cases over time, possible human losses, and the rate of recovery of patients, to make informed decisions about the number of necessary beds in hospitals, the introduction and type of quarantine measures, and the required threshold of vaccination of the population. Methods This study analyzed the onset of COVID-19 spread in countries such as China, Italy, Spain, the United States, the United Kingdom, Japan, France, and Germany based on publicly available statistical data. The change in the number of COVID-19 cases, deaths, and recovered persons over time was examined, considering the possible introduction of quarantine measures and isolation of infected people in these countries. Based on the data, the virus transmissibility and the average duration of the disease at different stages were evaluated, and a model based on the principle of recursion was developed. Its key features are the separation of active (nonisolated) infected persons into a distinct category and the prediction of their number based on the average duration of the disease in the inactive phase and the concentration of these persons in the population in the preceding days. Results Specific values for SARS-CoV-2 transmissibility and COVID-19 duration were estimated for different countries. In China, the viral transmissibility was 3.12 before quarantine measures were implemented and 0.36 after these measures were lifted. For the other countries, the viral transmissibility was 2.28-2.76 initially, and it then decreased to 0.87-1.29 as a result of quarantine measures. Therefore, it can be expected that the spread of SARS-CoV-2 will be suppressed if 56%-64% of the total population becomes vaccinated or survives COVID-19. Conclusions The quarantine measures adopted in most countries are too weak compared to those previously used in China. Therefore, it is not expected that the spread of COVID-19 will stop and the disease will cease to exist naturally or owing to quarantine measures. Active vaccination of the population is needed to prevent the spread of COVID-19. Furthermore, the required specific percentage of vaccinated individuals depends on the magnitude of viral transmissibility, which can be evaluated using the proposed model and statistical data for the country of interest.
机译：背景技术21世纪的主要医疗和社会挑战是Covid-19，由小冠状病毒SARS-COV-2引起。关键问题包括冠状病毒传播和检疫措施和人口疫苗接种的速度的速度。了解Covid-19传播法律，将能够评估所使用的检疫措施的有效性和合理性，以及确定克服这一危机所需的必要疫苗的必要疫苗。目的本研究旨在建立Covid-19的传播法，并使用它们开发数学模型，以预测随着时间的推移，可能的人类损失以及患者的恢复速度，以及患者的恢复率。关于医院必要床的数量，检疫措施的引入和类型的知情决定，以及人口疫苗接种所需的阈值。方法本研究分析了Covid-19在中国，意大利，西班牙，美国，英国，日本，法国和德国等国家的展开的展开，基于公开的统计数据。考虑到可能引入可治区措施和这些国家感染者的孤立，审查了Covid-19案件，死亡和收回人数的变化。基于数据，评估病毒传染性和疾病的平均持续时间，并开发了基于递归原理的模型。其关键特征是将活性（非分层）受感染者分离成一个不同的类别，并根据疾病中疾病的平均持续时间和前几天人群中这些人的浓度预测它们的数量。结果SARS-COV-2传导性和CoVID-19持续时间的特定值估计不同国家。在中国，在实施检疫措施之前，病毒传播性为3.12，并提升这些措施后0.36。对于其他国家，最初的病毒传播性为2.28-2.76，然后在检疫措施下降至0.87-1.29。因此，如果总群的56％-64％的疫苗接种或幸存下来，可以抑制SARS-COV-2的扩散将被抑制。结论与以前在中国使用的人相比，大多数国家采用的检疫措施太弱。因此，预计Covid-19的传播将停止，并且这种疾病将停止自然或由于检疫措施。需要积极接种群体以防止Covid-19的传播。此外，接种疫苗的个体所需的特异性百分比取决于病毒传播性的大小，可以使用所提出的模型和统计数据来评估感兴趣的国家。

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