Trend and forecasting of the COVID-19 outbreak in China

Dear editors,

Very recently, a letter in Journal of Infection reported the outbreak of the novel cornonavirus from Dec. 2019 in China, especially in Hubei province.¹ This novel cornonavirus may originate from the bat,² is just named as the COVID-19 by the World Health Organization (WHO). The COVID-19 outbroke from Wuhan, the capital of Hubei province, has spread to other provinces of China and even other countries.³ Strong human-to-human transmission is established.⁴ Until Feb. 11, 2020, there have been 44653 cases of COVID-19 infections confirmed in mainland China, including 1113 deaths. To prevent and control the spread of the epidemic, many strategies are needed.⁵ Predicting the trend of the epidemic are quite important to the allocation of medical resources, the arrangement of production activities, and even the domestic economic development all over China. Therefore, it is very urgent to use the latest data to establish an efficient and highly suitable epidemic analysis and prediction model according to the actual situation, and then to give reliable predictions, which could provide an important reference for the government to formulate emergency macroeconomic decisions and medical resources allocation.

Recently, the susceptible-exposed-infectious-recovered (SEIR) or other similar models 6, 7 are used to forecast the potential domestic and international spread of this COVID-19 epidemic with parameters estimated from other sources.The real situation could be much more complicated and changing all the time. Especially, with the implementation of the Chinese government’s multiple epidemic control policies, the control of nationwide epidemic has become obvious. However, the medical supplies in Hubei will still affect the implementation of national policies. In this letter, we present the current situation of the epidemic, predict the ongoing trend with data driven analysis, and estimate the outbreak size of the COVID-19 in both Hubei and other areas in mainland China.

The data of the epidemic are listed in Table 1 and also graphically shown in Fig. 1 , in which “China” is used to denote the mainland China, and “Other” mainland China other than Hubei province. The data includes the daily confirmed(suspected) infections, totally confirmed(suspected) infections, daily deaths, and total deaths from Jan. 20, to Feb. 11, 2020, reported by the National Health Commission of the Republic of China (NHC),⁸, and Health Commission of Hubei Province (HCH).⁹ Jan. 20, 2020, containing all the cases reported from 0 to 24, is the zeroth day in this letter, and then others are implied. The total number of suspected cases reaches the peak value on the 19th day (Feb. 8), and then drops rapidly. Notice that, until Feb. 11, 2020, almost all the cases of deaths (1068/1113, 96%,) locates in Hubei province, which reveals the epidemic in Hubei is much more serious than that in the other areas of China. On the hand, it states the strict quarantine and limitation on population mobility have effectively prevented outbreaks in other provinces of China.

Table 1.

The data of epidemic caused by the COVID-19 pneumonia in the mainland China and Hubei, including (A) daily infections, (B) daily deaths, (C) total infections, (D) total deaths, (E) daily and (F) total suspected cases.

Date	China						Hubei
	A	B	C	D	E	F	A	B	C	D
2020/1/20	77	2	291	6	27	54	72	2	270	6
2020/1/21	149	3	440	9	26	37	105	3	375	9
2020/1/22	131	8	571	17	257	393	69	8	444	17
2020/1/23	259	8	830	25	680	1072	105	7	549	24
2020/1/24	444	16	1287	41	1118	1965	180	15	729	39
2020/1/25	688	15	1975	56	1309	2684	323	13	1052	52
2020/1/26	769	24	2744	80	3806	5794	371	24	1423	76
2020/1/27	1771	26	4515	106	2077	6973	1291	24	2714	100
2020/1/28	1459	26	5974	132	3248	9239	840	25	3554	125
2020/1/29	1737	38	7711	170	4148	12,167	1032	37	4586	162
2020/1/30	1982	43	9692	213	4812	15,238	1220	42	5806	204
2020/1/31	2102	46	11,791	259	5019	17,988	1347	45	7153	249
2020/2/1	2590	45	14,380	304	4562	19,544	1921	45	9074	294
2020/2/2	2829	57	17,205	361	5173	21,558	2103	56	11,177	350
2020/2/3	3235	64	20,438	425	5072	23,214	2345	64	13,522	414
2020/2/4	3887	65	24,324	490	3971	23,260	3156	65	16,678	479
2020/2/5	3694	73	28,018	563	5328	24,702	2987	70	19,665	549
2020/2/6	3143	73	31,161	636	4833	26,359	2447	69	22,112	618
2020/2/7	3399	86	34,546	722	4214	27,657	2841	81	24,953	699
2020/2/8	2656	89	37,198	811	3916	28,942	2147	81	27,100	780
2020/2/9	3062	97	40,171	908	4008	23,589	2618	91	29,631	871
2020/2/10	2478	108	42,638	1016	3536	21,675	2097	103	31,728	974
2020/2/11	2015	97	44,653	1113	3342	16,067	1638	94	33,366	1068

Fig. 1.

Varies of the COVID-19 epidemic (Jan. 20–Feb. 11, 2020) in China, with (a) total and (b) daily suspected and confirmed cases, (c) total and (d) daily deaths, (e) death rate, and (f) deaths in China other than Hubei.

We use function $h\left(t\right)=A[{(1+e^{-kx})}^{-1}-{(1+e^{k-kx})}^{-1}]$ to describe the data of daily infections and deaths in Hubei, where $x=(t+0.5-t_{\mathrm{T}})$ with t denoting the day, and t _T representing the turning point; A and k are the parameters and determined by the data together with t _T. The cumulative data of infections or deaths are obtained by the integration over h(t). For the epidemic in the other areas of China, the data of infections shows an asymmetric character, and then will be described as $s\left(t\right)=B\exp [-(x+k_1{e}^{-x/k_1}\left)\right],$ where $x=t-t_{\mathrm{T}}$; the parameters B, k ₁, and k ₂ together with t _T, are then determined by fitting to the data.

Fig. 2 shows the fit and trend predictions to the total infections and deaths in Hubei and China other than Hubei. The extracted turning point of the infections in Hubei is the 17th day, namely, Feb. 6, 2020. The epidemic in Hubei is predicted to end after Mar. 10, 2020. We estimated that the epidemic is to end up with a total of 39, 000 infections in Hubei, not including the clinically diagnosed cases since Feb. 12, which may enlarge the prediction by 1.4 times. With considered data, namely, data from Jan. 20 to Feb. 11, the average errors are bout 166 and 190 for the fits to describe the daily and cumulative infections in Hubei, respectively, corresponding to 8.6% and 1.6% for the average relative errors, respectively.

Fig. 2.

Data (Jan. 20–Feb. 11, 2020) and fits of the infections and deaths in China; the black circle denotes the data, and the dotted line the predicted trend; the turning points of daily infections and deaths in Hubei are predicted to be Feb. 6, and Feb. 12, 2020, respectively, and Feb. 1 for daily infections in China other than Hubei.

Fig. 2 (b) and (e) shows the estimations of the total and daily deaths in Hubei. The predicted turning point is Feb. 12, 2020. The total deaths is estimated to be 2250. Notice the distribution of the daily deaths is delayed about 5∼6 days compared with the that of the daily infections. The average errors are bout 4 and 22 for the model to describe the daily and cumulative death numbers, respectively, corresponding to the relative errors 8.6% and 6.2%, respectively.

The numbers of the daily and total infections in China other than Hubei are showed in Fig. 2(c) and 2(f), respectively. The extracted turning point is Feb. 1, 2020 and the epidemic is expected to end on the 45th day, namely, on Mar. 5, 2020. The estimated number of cumulative infections is about 12,600 in China other than Hubei. With the data in the considered period, the average errors are bout 41 and 58 for this model to describe the daily and total cumulative infections, and the corresponding relative errors are about 8.4% and 1.2%, respectively. Due to the minority of the statistical data in deaths of China other than Hubei (45 until Feb. 11, 2020, see Fig. 1(f)), we did not parameterize this data, and hence did not give a trend prediction.

The COVID-19 epidemic in China is predicted to end after Mar. 20, 2020, and cause 52,000–68,000 infections and about 2400 deaths. However, the data trends show that the quick and active strategies to reduce human exposure taken in China, such as limitation on population mobility and interpersonal contact rates, strict quarantine on migrants, have already had good impacts on control of the epidemic. Now the outbreak and deaths of the COVID-19 epidemic are mainly in Hubei province. After this letter has been written, the Hubei reported 14,840 confirmed infections (including 13,332 clinically diagnosed cases) on Feb. 12, 2020, which is almost 9 times greater than the data of the previous day. The huge fluctuation is due to the changing of diagnostic criteria in Hubei. And this clinical criteria taken in Hubei is expected to play an active and important role in controlling the outbreak and death rate.

Declaration of Competing Interest

The authors declare no conflict of interest.