论文标题
COVID-19的数学模型，具有因素感染率的依赖性变化率：适用于大韩民国
A mathematical model of the COVID-19 pandemic dynamics with dependent variable infection rate: Application to the Republic of Korea
论文作者
论文摘要
这项工作构建，分析和模拟了新的隔室SEIR型模型，以用于当前Covid-19的动力学和潜在控制。这项工作的新颖性是两个方面。首先，人口根据其遵守疾病控制指令（锁定，地面庇护所，面具/面罩，身体距离等）分为完全遵守的人，以及那些部分遵守指令的人，或者必须部分遵守指令，或者必须是移动的（例如医务人员）。这种分裂间接地反映了这些措施的质量和一致性。这允许评估控制措施的总体有效性及其放松或收紧疾病扩散的影响。其次，直接影响感染率的足够接触率是未知的模型之一，因为它可以通过差异包含来跟踪种群行为的变化以及各种疾病治疗方式的有效性。使用基于非标准凸的方法证明存在，独特性和阳性结果。作为一个案例研究，模拟了大韩民国（韩国）的大流行爆发。通过将模型预测与韩国大流行的前100天的偏差最小化与报告的数据的偏差来找到模型参数。模拟表明，该模型在随后的75天内准确捕获了大流行动力学，从而对模型预测及其未来的使用提供了信心。特别是，该模型预测，大约40％的感染未记录，这意味着无症状的感染会静静地促进，但基本上会导致该疾病的传播，这表明需要更多广泛的无症状测试。
This work constructs, analyzes, and simulates a new compartmental SEIR-type model for the dynamics and potential control of the current COVID-19 pandemic. The novelty in this work is two-fold. First, the population is divided according to its compliance with disease control directives (lockdown, shelter-in-place, masks/face coverings, physical distancing, etc.) into those who fully comply and those who follow the directives partially, or are necessarily mobile (such as medical staff). This split, indirectly, reflects on the quality and consistency of these measures. This allows the assessment of the overall effectiveness of the control measures and the impact of their relaxing or tightening on the disease spread. Second, the adequate contact rate, which directly affects the infection rate, is one of the model unknowns, as it keeps track of the changes in the population behavior and the effectiveness of various disease treatment modalities via a differential inclusion. Existence, uniqueness and positivity results are proved using a nonstandard convex analysis-based approach. As a case study, the pandemic outbreak in the Republic of Korea (South Korea) is simulated. The model parameters were found by minimizing the deviation of the model prediction from the reported data over the first 100 days of the pandemic in South Korea.The simulations show that the model captures accurately the pandemic dynamics in the subsequent 75 days, which provides confidence in the model predictions and its future use. In particular, the model predicts that about 40% of the infections were not documented, which implies that asymptomatic infections contribute silently but substantially to the spread of the disease indicating that more widespread asymptomatic testing is necessary.
