JMIR Publications

ABSTRACT

Background:

In the fight against the pandemic of COVID-19, it is important to be quick to detect changes in the rate of spread and to be precise to predict the future. We have succeeded in formulating a new indicator based on daily number of infected people from publicly available data, which enables us to do the both. We show the validity of the indicator by demonstrating that a universal analysis of current status of COVID-19 spreading over countries can predict effects of measures such as the blockage of cities and social distancing, signs of new spread, and possible regional dependence in the formation of herd immunity.

Objective:

Global spread of COVID-19 has resulted in significant human and economic losses worldwide. In order to prevent the spread of infection, it is necessary to restrict social activities by policies such as the blockade of cities and the prohibition of assembly. For the effective implementation of these policies, it is necessary to ascertain the status of spread and to estimate the trend of spread accurately. However, it is often difficult to grasp the severity of spread and estimate the trend by using model calculations because the implementation criteria of PCR testing vary from country to country and a high level of expertise is required to adjust model parameters according to the circumstances of each country. The threat of COVID-19 has spread over countries which do not have the high-level computing resources, and the development of means to ascertain the status of spread accurately without relying on specific models has become an urgent issue.

Methods:

In this study, we introduce a new indicator called the K value defined by K(d) = 1−N(d − 7)/N(d), where d is the number of days from the reference date, and N(d) and N(d−7) are the total number of infected people on days d and (d−7), respectively. Since N(d) is greater than N(d−7) during the period from the initiation of spread to convergence, K takes a value between 0 and 1. Without loss of generality, the daily evolution of N(d) can be expressed with a time dependent exponential factor a(d) as N(d + 1) = exp(a(d))N(d). Our assumption is that a(d) can be expressed by a geometric series with a constant dumping factor k, namely, a(d+1) = ka(d). The simulation study under this assumption found that K can be approximated by a first order linear function of d in a wide range (0.25 < K < 0.9) and the input value of k can be reproduced by k = 1 + 2.88K’, where K’ is a slope of a straight line obtained by the fit (Appendix). The validity of the assumption has been checked and confirmed by analyzing the existing data (1–3) as demonstrated in the report. The quotient of |K/K’| gives a good estimation for a time period for COVID-19 spread to converge, and an upward change of the K trajectory indicates a new outbreak. By updating the K value in real time using daily input data, we can identify the current status of spread, estimate the future status of spread, and detect signs of new spread at an early stage.

Results:

The analysis using K was first applied to China. The K values is closely approximated by a straight line with a slope (K’) of −0.0402±0.0008/d. The linearity of K is also prominent in the United States. After a high K level period indicating successive infectious explosions from mid to late March, the K has continued to decline with a uniform rate of K’ = −0.0237±0.0003/d in the fitting region of 0.25 < K < 0.90. In a region of K < 0.25, transition of K can be estimated with a constant dumping factor k calculated from K’. Comparison between the data points and the model estimations tells us that the pace of convergence became higher in China in the terminating phase, while it was significantly reduced in USA. In Italy, where COVID19 started to spread first in Europe, K’ was −0.0142 ± 0.0004/d from March 1 to 23 indicating a slow pace of convergence, but the pace was improved after March 24 resulting in K’ = −0.0263 ± 0.0006/d. This improvement is most likely due to the containment policy implemented in early March, including the blockade of cities. Countries’ policies changed the K’ values in both Germany and Sweden too. It is quite important to minimize the period of the early stages with K’ ∼ −0.007/d. One week delay of implementation of countermeasures will double the total number of infected people. In Asian countries close to China, after the first wave originated in China, and the subsequent spread in synchronized with the worldwide spread can be observed as the upward change in K trajectories. We obtained K’ = −0.0283±0.0006/d in Japan. The slope is milder than those of Taiwan (K’ = −0.0524 ± 0.0026/d) and South Korea (K’ = −0.0820 ± 0.0042/d and K’ = −0.0378 ± 0.0024/d), reflecting the difference in the strictness and efficiency of countermeasures. However, it is steeper than those of European countries with more strict social restrictions than Japan. The relatively high absolute K’ values even in the early stages are common in many Asian countries.

Conclusions:

As the spread of COVID-19 worldwide progresses, it is important not only to protect human lives, but also to minimize social losses due to economic paralysis by detecting signs of spread at an early stage and predicting future trends accurately. We have demonstrated that the value of K and its slope of K’ are crucial for understanding the spread status of COVID19 for these purposes. Thanks to linear dependence on the elapsed days and stability due to oneweek interval for the calculation, extrapolation of the K trajectory and prediction of the future trend of COVID-19 are easy. Analyses with the K and K’ values will help us to implement appropriate measures in a timely manner and evaluate their effects. Moreover, since the K’ is related with a fundamental factor k, a global antibody testing survey together with a systematic study of K’ may reveal the underlying reasons for regional differences in infection rate and mortality of COVID-19 between Europe and Asia. Also, as evidenced by the comparison with the SI model calculations, the linearity of the K value is not trivial but is most likely to be caused by several consecutive infectious explosions. Focusing on the change in the value of K will help to improve and refine epidemiological models of infectious diseases with the same tendency as COVID-19.