Kuniya Toshikazu, Inaba Hisashi
Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan.
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan.
AIMS Public Health. 2020 Jul 6;7(3):490-503. doi: 10.3934/publichealth.2020040. eCollection 2020.
The pandemic coronavirus disease 2019 (COVID-19) has spread and caused enormous and serious damages to many countries worldwide. One of the most typical interventions is the social distancing such as lockdown that would contribute to reduce the number of contacts among undiagnosed individuals. However, prolongation of the period of such a restrictive intervention could hugely affect the social and economic systems, and the outbreak will come back if the strong social distancing policy will end earlier due to the economic damage. Therefore, the social distancing policy should be followed by massive testing accompanied with quarantine to eradicate the infection.
In this paper, we construct a mathematical model and discuss the effect of massive testing with quarantine, which would be less likely to affect the social and economic systems, and its efficacy has been proved in South Korea, Taiwan, Vietnam and Hong Kong.
By numerical calculation, we show that the control reproduction number is monotone decreasing and convex downward with respect to the testing rate, which implies that the improvement of the testing rate would highly contribute to reduce the epidemic size if the original testing rate is small. Moreover, we show that the recurrence of the COVID-19 epidemic in Japan could be possible after the lifting of the state of emergency if there is no massive testing and quarantine.
If we have entered into an explosive phase of the epidemic, the massive testing could be a strong tool to prevent the disease as long as the positively reacted individuals will be effectively quarantined, no matter whether the positive reaction is pseudo or not. Since total population could be seen as a superposition of smaller communities, we could understand how testing and quarantine policy might be powerful to control the disease.
2019年大流行冠状病毒病(COVID-19)已蔓延并给全球许多国家造成了巨大而严重的破坏。最典型的干预措施之一是社交距离措施,如封锁,这有助于减少未确诊个体之间的接触数量。然而,这种限制性干预措施期限的延长可能会对社会和经济系统产生巨大影响,并且如果由于经济损害而过早结束强有力的社交距离政策,疫情将会反弹。因此,在实施社交距离政策之后应进行大规模检测并辅以隔离措施以根除感染。
在本文中,我们构建了一个数学模型,并讨论了大规模检测并辅以隔离措施的效果,这种措施不太可能影响社会和经济系统,并且其有效性已在韩国、台湾、越南和香港得到证明。
通过数值计算,我们表明控制再生数相对于检测率单调递减且向下凸,这意味着如果原始检测率较低,提高检测率将极大地有助于减小疫情规模。此外,我们表明,如果没有大规模检测和隔离措施,日本在解除紧急状态后COVID-19疫情有可能复发。
如果我们已进入疫情爆发阶段,只要对呈阳性反应的个体进行有效隔离,无论阳性反应是否为假阳性,大规模检测都可能是预防该疾病的有力工具。由于总人口可视为较小社区的叠加,我们可以理解检测和隔离政策对控制疾病的强大作用。