论文标题
关于冠状病毒感染和数据分析的隔离模型
On a quarantine model of coronavirus infection and data analysis
论文作者
论文摘要
试图通过引入严格的隔离措施来遏制冠状病毒的传播显然在不同国家的影响不同：虽然据报道，在中国和韩国，新病例的数量已减少，但在意大利和欧洲其他国家仍显示出显着增长。在此简短说明中，我们努力通过数学建模来评估隔离措施的效率。我们不是经典的SIR模型，而是引入了一种新的感染进展模型，假设所有感染者在孵化期之后都孤立，以使他们无法感染其他人。该模型中的疾病进展取决于基本的繁殖数$ \ Mathcal {r} _0 $（在孵化期内新感染的个体的数量），这与标准SIR模型相比有所不同。如果$ \ MATHCAL {R} _0> 1 $，则被指数级的潜在感染者数量增长。但是，如果$ \ MATHCAL {R} _0 <1 $（例如，由于公共当局施加的隔离措施和联系限制），则被指数衰减的数量。然后，我们考虑有关不同国家疾病发展的可用数据，以表明存在三种可能的模式：增长动态，增长时间动态和斑驳的动态（增长 - 增长）。对中国和韩国数据的分析表明，在引入限制措施后约10天达到感染的峰值（每日病例最大）。在此期间，感染总数的增长率逐渐减少。但是，意大利的增长率仍然指数。可以说，这表明引入的隔离是不够的，需要采取更严格的措施。
Attempts to curb the spread of coronavirus by introducing strict quarantine measures apparently have different effect in different countries: while the number of new cases has reportedly decreased in China and South Korea, it still exhibit significant growth in Italy and other countries across Europe. In this brief note, we endeavour to assess the efficiency of quarantine measures by means of mathematical modelling. Instead of the classical SIR model, we introduce a new model of infection progression under the assumption that all infected individual are isolated after the incubation period in such a way that they cannot infect other people. Disease progression in this model is determined by the basic reproduction number $\mathcal{R}_0$ (the number of newly infected individuals during the incubation period), which is different compared to that for the standard SIR model. If $\mathcal{R}_0 >1$, then the number of latently infected individuals exponentially grows. However, if $\mathcal{R}_0 <1$ (e.g.~due to quarantine measures and contact restrictions imposed by public authorities), then the number of infected decays exponentially. We then consider the available data on the disease development in different countries to show that there are three possible patterns: growth dynamics, growth-decays dynamics, and patchy dynamics (growth-decay-growth). Analysis of the data in China and Korea shows that the peak of infection (maximum of daily cases) is reached about 10 days after the restricting measures are introduced. During this period of time, the growth rate of the total number of infected was gradually decreasing. However, the growth rate remains exponential in Italy. Arguably, it suggests that the introduced quarantine is not sufficient and stricter measures are needed.
