Time interval between orders of magnitude reflects on Covid-19

中文版：《各國新肺案例數量級增長用時統計及相關思考》

 

1. Days it takes for the case to grow by an order of magnitude

Before doing the analysis, this article needs to define a concept called TIM:

In the countries that number of Covid-19 cases exceeds 10,000, the dates that the cases broke through an order of magnitude each time is counted to obtain the time interval of cases increased by every of the order of magnitude in the country, which the time interval is defined as TIM. (Data till 4/18).

Or other style:

Table 1. Average TIM value

Number of cases	Ave. TIM	Notes
10-100	9 days
100-1000	9 days	8 days except Japan.
1000-10000	15 days	9 days if only count first 9 countries.
10000-100000	17 days	USA, 8 days.

Many countries did some efforts to respond the epidemic when the number of cases reached to 1000. Therefore, during the increasing of 1000 to 10000 and then to 100000, the TIM value was decreased.

According to average TIM value and the specific situation of each country, if no appropriate intervention was applied, the TIM value might be around 8 to 9 days.

 

2. Possible values of R₀ according to the cases and propagation

Since the calculation of R₀ is difficult for non-professional people, the following content will make a general deduction according to the definition of R₀ to let more people understand. But please well-know that: this is only a rough approximation and cannot be used as a rigorous calculation method.

The formula for calculating R₀ reported^[1]:

R₀ = (1 + rT_L—)( 1 + rT_I—)

Where r represents the growth rate in exponential growth model,T_L— represents the average length of the incubation period of an infected person,T_I— represents the average length of the infected person become infectious after be infected, since it is difficult to get this value, it is also calculated by formulaT_I— = SI— –T_L—, SI is for Serial Interval or Generation Time, it means: the interval between the time a person is infected and the time another person get infected by the infected person.

The following deduction does not use the above calculation formula, But the concept of SI is needed. Assume that SI=1, R₀=x, x is the value of R₀, that is, the infected person can infect another x individuals and no longer infect others the next day after being infected.

Thus, it is easy to obtain the assumed TIM value when SI = 1 by the obtained series of values calculated by the exponential growth model. Then multiply the assumed TIM value by SI, deduced TIM value could be obtained.

Table 2. deduced TIM value

R0	TIM (SI=8.4*1)	TIM (SI=7.5*2)	TIM (SI=5*3)	TIM (SI=4*3)	TIM (SI=3*3)
2	26.88	24.00	16.00	12.80	9.60
3	16.80	15.00	10.00	8.00	6.00
4	12.60	11.25	7.50	6.00	4.50
5	11.45	10.23	6.82	5.45	4.09
6	10.80	9.64	6.43	5.14	3.86
10	8.40	7.50	5.00	4.00	3.00

*1，Data from a paper published on The Lancet^[2];

*2，Data from a paper published on NEJM^[3];

*3，This article assumes some SI values. It should be noted here that in the above R₀ calculation formula, the incubation period was thoughts does not infect others, however, in this article it is considering that possibility of infecting others in the incubation period cannot be ruled out. At present, the incubation period is generally considered to be 2 to 11 days, so the values 3, 4, and 5 are selected as assumed SI value, to observe what TIM value will be obtained.

The comparison between table 1 and table 2 shows that:

• If SI=8.4，the actual R₀ might be 10 or even higher;
• If SI=7.5，the actual R₀ might also higher than 6;
• If SI=5，the actual R₀ could be between 3 and 4.

P.S. You can also use this table to roughly calculate the current R₀ value in your country/region.

 

3. Summary

According to the general gradual graph, the number of confirmed cases increases rapidly, but every eight to nine days increased for an order of magnitude may exceed people’s imagination. In fact, some countries and regions already applied certain preparations, and people also had some precautions. If there is no interference at all, the growth rate might be much faster.

Previously, WHO report R₀ = 2-2.5^[4]. Recently, some news said new research results indicate that R₀ may reach up to 5 (the corresponding papers were not found^[5,6]), but it has not been confirmed on a large scale, and the current authoritative announcements about R₀ are 1.4-2.5^[7], 2.24-3.58^[8], 1.5-3.5^[9,10,11]. Based on the rapid growth earlier (TIM = 8-9 days, and even <7 days in some countries), the SI value could be reversed with Table 2. If R₀ is between 2-3, then the SI should be in 3-5 days.

Earlier reports of the Wuhan cases concluded that the incubation period of covid-19 was 6.4 days. Later, researchers at the Johns Hopkins University Bloomberg School of Public Health found that the median incubation period was 5.1 days. Together with the results shown in this article when SI set as 3-5, a conclusion can be drawn: Covid-19 is very likely to infect people during the incubation period. Therefore, isolation measures should not only be taken against people confirmed as infected to covid-19 or people with fever symptoms, but also to be wary of strangers. As it is impossible to identify latent patient in the crowd, wearing mask in a correct way and necessary disinfection actions are very necessary. According to the situation so far, China, Japan and South Korea have done well in this regard. However, the author thought that Japan should take tougher measures in the current circumstances.

In addition, since SI may be less than`T<sub>L</sub> result a negative`T_I, the existing R0 calculation formula may need to be revised.

At the end, again, this article is not rigorous, just to understand some concepts from the view of public.

 

References:

1. 如何計算基本再生數R0？
2. Wu, J. T., Leung, K., & Leung, G. M. (2020). Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study. The Lancet. 2020; S0140-6736(20)30260-9.
3. Li, Q., Guan, X., Wu, P., Wang, X., Zhou, L., Tong, Y., … & Xing, X. (2020). Early transmission dynamics in Wuhan, China, of novel coronavirus–infected pneumonia. New England Journal of Medicine.
4. Report of the WHO-China Joint Mission on Coronavirus Disease 2019 (COVID-19), 16-24 February 2020.
5. COVID-19 的傳染數是以前認為的兩倍.
6. COVID-19專題：關於R0，你想知道的都在這裡.
7. Statement on the meeting of the International Health Regulations (2005) Emergency Committee regarding the outbreak of novel coronavirus (2019-nCoV)– WHO, January 23, 2020.
8. Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak– Jan. 30, 2020.
9. Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic prediction– Jonathan M. Read et al, Jan. 23,2020.
10. Early Transmissibility Assessment of a Novel Coronavirus in Wuhan, China– Maimuna Majumder and Kenneth D. Mandl, Harvard University – Computational Health Informatics Program – Posted: 24 Jan 2020 Last revised: 27 Jan 2020.
11. Report 3: Transmissibility of 2019-nCoV– 25 January 2020 – Imperial College London‌.