COVID-19 information propagation dynamics in the Chinese Sina-microblog

1.   Introduction

The rapidly evolving novel coronavirus (COVID-19) has received considerable social attention. Major news items combined have generated quite strong fluctuations in public opinions. For example, when Nanshan Zhong, a well-known expert in infectious disease control, confirmed that the COVID-19 could be transmitted from human to human on January 20, 2020 ^[1], the outbreak-related topics grew exponentially and the personal protection equipment such as surgical masks was instantly in urgent need and in short supply ^[2]. Understanding how these emerging topics spread in social media to alter the public behaviors is important to help designing effective communication strategies for rapid implementation of public health interventions.

To our best knowledge, there is no appropriate model framework that can be used to analyze multiple-information propagation during a major public health emergency. In consideration of the urgent need to develop theoretically sounding and practical useful technologies to help effective communications of public health interventions, we propose a multiple-information susceptible-discussing-immune model (M-SDI) based on the discussion quantity which under multiple related topics to analyze the public opinion propagation of the COVID-19. In particular, we consider the characteristic user behavior that users may participate in the discussion on different microblogs subordinate to different topics.

Sina-microblog is the most popular microblogging service in China ^[3] and public opinion concentrates outbreak on that platform. Figure 1 shows the whole process of COVID-19 information propagation in Sina-microblog. Many original post owners can post multiple microblogs related to the epidemic in one of multiple topics. Take CCTV News and China Daily for example. CCTV News reports on multiple topics, while China Daily focuses on a particular topic, and both of them can be discussed by users who are interested in these Weibos, and the relevant discussion can resume in the Sina-microblog later, leading to a multi-level information diffusion process. All users (discussants) can choose to discuss only one Weibo or multiple Weibos, and information propagates through one Weibo or multiple Weibos. This promotes the COVID-19 information dissemination rapidly.

Figure 1.  Multiple information discussion propagation of the COVID-19.

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2.   Related literature

Traditionally, researches of scholars on information mainly focused on single information, and the publication of a large number of papers began with the study of rumors. Considering rumors are similar to epidemiology in several ways, many scholars used susceptible-infected (SI) model ^[4,5], susceptible-infected-recovered (SIR) model ^[6,7], susceptible-infected-exposed-recovered (SEIR) model ^[8,9] and susceptible-infected-susceptible (SIS) ^[10] model to represent rumor propagation and address relevant issues. Then, classical models were improved to be more targeted and effective. In 2012, Zhao et al. ^[11] developed a new rumor spreading model called susceptible-infected-hibernator-removed (SIHR) model introducing a new kind of people-Hibernators in order to reduce the maximum rumor influence. In 2014, Zhao et al. ^[12] added the refutation mechanism in homogeneous social networks to the basic model, which could help authorities reduce the maximum influence of the rumor. In 2015, Zhang et al. ^[13] studied the cumulative effects of memory on rumor spreading and proposed a model that examined how the memory affected rate changes over time in an artificial network and a real social network. Chen et al. ^[14] studied the effect of the nodes' role in network on rumor's suppression. Zhang et al. ^[15] developed the dynamic 8-state ignorance-carrier-spreader-advocate-removal (ICSAR) rumor propagation model to study the function of each influencing factor, which could improve the efficiency of rumor refutation and make emergency plans. Huang et al. ^[16] constructed a model that took the impact of rumor refuting by the affected enterprise, a microblogging opinion leader and microblogging platform into account. Trpevski D et al. ^[17], Qian et al. ^[18], Wang et al. ^[19], Wang et al. ^[20], Cheng et al. ^[21], Liu et al. ^[22] also extended basic models to study the spread of rumors and had gotten substantial progress.

With the improvement of the academic level, researches about information dissemination are not restricted to rumors. In 2012, Xiong et al. ^[23] proposed a susceptible-contacted-infected-refractory (SCIR) diffusion model, which contained four possible states to characterize information propagation on online microblogs. Rui et al. ^[24] proposed a susceptible-potential-infective-removed (SPIR) model that analyzed the diffusion process based on the discrete-time to avoid repeatedly calculating susceptible nodes. And in 2019, we ^[25] proposed an epidemic model called susceptible-forwarding-immune (SFI) to capture a single information propagation trend in the Sina-microblog.

But in complex social networks, it is rare for single information to exist independently. In other words, multiple information propagation is more common. In 2018, Zan et al. ^[26] studied the double rumors spreading with different launch time and introduced two kinds of model: double-susceptible-infected-recovered (DSIR) model and comprehensive-DSIR (C-DSIR) model, which focused on the interaction from old rumor to new rumor and the propagation of two rumors posted successively. By investigating states-vectors expressions and attraction of different rumors, they provided the double-rumors dissemination mechanism finally.

Different from previous work, in this paper, we not just consider the behavior of users under one information or two information. Particularly, we focus on the feature that users may re-enter the next related information under different topic after finishing a discussion of one certain information. By analyzing multiple-information propagation mechanism about COVID-19, we can distinctly predict evolution of public opinion.

3.   Public opinion data of COVID-19 in Chinese Sina-microblog

Since the outbreak of COVID-19, around 4000 major topics appeared in Sina-microblog and the representative topics included #Latest outbreak map#, #Real-time information on joint epidemic prevention and control#, #Wuhan diary#, etc. Figure 2 shows the cumulative discussion quantity of 4059 topics from December 31, 2019 to February 27, 2020, where the ordinate is the logarithm of the cumulative discussion quantity. It can be roughly seen that during the period from December 31, 2019 to January 15-17, 2020, there was only a certain amount of hot topics of COVID-19, however, from January 18-20, 2020, the hot topics about the epidemic kept emerging dramatically.

Figure 2.  The discussion quantity of 4059 hot topics about COVID-19.

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Table 1 gives the final cumulative discussion quantity of 35 typical topics as of February 27, 2020, among which, #Cheer up! Wuhan# has the highest discussion quantity of $355.26\times10^{5}$. And some of the hot topics like #Nationally confirmed cases of novel coronavirus pneumonia#, #Doctor Wenliang Li passed away# have a discussion quantity over $10\times10^{5}$. Since each hot topic is a part of the entire epidemic event, we pay attention to the total number of the entire COVID-19 information propagation, as shown in Table 2, where 'C' denotes the sum of cumulative discussion. We removed part of data caused by fans of stars to ensure the objectivity and avoid the effect of "water army".

Table 1.  Some hot topics for COVID-19 in China.

Date	Typical hot topics	Discussion(*$10^{5}$)
2019.12.31	#Pneumonia of unknown cause was found in Wuhan#	1.01
2020.1.20	#Nanshan Zhong confirms the human-to-human transmission of the new coronavirus pneumonia#	3.89
2020.1.21	#291 cases of novel coronavirus pneumonia have been confirmed in China#	1.48
2020.1.22	#Nationally confirmed cases of novel coronavirus pneumonia#	29.03
	#The COVID-19 is not resistant to alcohol and high temperatures#	4.97
2020.1.23	#Cheer up! Wuhan#	355.26
	#Wuhan Sealed off#	6.07
2020.1.25	#Latest outbreak map#	25.21
2020.1.26	#5 million people left Wuhan#	4.31
	#Wuhan#	5.41
	#Wuhan diary#	43.69
2020.1.28	#Real-time information on joint epidemic prevention and control#	3.71
2020.1.29	#The outbreak is still spreading#	2.49
2020.1.30	#The World Health Organization#	2.23
2020.1.31	#Shuanghuanglian can inhibit the new coronavirus#	5.41
	#The charity worker Han Hong#	3.11
2020.2.1	#Doctor Wenliang Li#	2.00
2020.2.2	#Huoshenshan hospital completed#	3.01
2020.2.4	#Hand-written encouragement relay#	135.28
	#There is no spring that does not come#	4.03
2020.2.6	#Vice governor of Hubei responds to citizens' asking for help online#	3.92
2020.2.7	#Doctor Wenliang Li is still under rescue#	4.40
	#Doctor Wenliang Li passed away#	13.79
	#Wuhan central hospital#	2.32
2020.2.8	#Record the anti-epidemic time#	3.29
2020.2.9	#CCTV Lantern Festival special program#	2.71
2020.2.10	#Fight against the epidemic clocking action#	104.38
2020.2.12	#Xinjiang doctors in Wuhan#	1.68
2020.2.13	#How to save masks scientifically#	20.48
2020.2.14	#Valentine's day under the epidemic#	38.93
2020.2.15	#The PK game of cooking food at home#	20.75
2020.2.19	#Easy epidemic prevention station#	13.99
2020.2.21	#Epidemic prevention and anti-epidemic east in action#	6.24
2020.2.23	#It depends on immunity#	3.54
2020.2.25	#The smile under a mask#	18.26

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Table 2.  The cumulative discussion quantity of COVID-19.

Date	2019.12.31	2020.1.1	2020.1.2	2020.1.3	2020.1.4	2020.1.5	2020.1.6
C (*$10^{5}$)	0.87	0.96	1.09	1.18	1.23	1.35	1.43
Date	2020.1.7	2020.1.8	2020.1.9	2020.1.10	2020.1.11	2020.1.12	2020.1.13
C (*$10^{5}$)	1.44	1.49	1.68	1.72	1.77	1.78	1.80
Date	2020.1.14	2020.1.15	2020.1.16	2020.1.17	2020.1.18	2020.1.19	2020.1.20
C (*$10^{5}$)	1.84	2.04	2.15	2.26	3	4	14
Date	2020.1.21	2020.1.22	2020.1.23	2020.1.24	2020.1.25	2020.1.26	2020.1.27
C (*$10^{5}$)	34	76	238	319	378	434	470
Date	2020.1.28	2020.1.29	2020.1.30	2020.1.31	2020.2.1	2020.2.2	2020.2.3
C (*$10^{5}$)	503	543	578	624	696	756	787
Date	2020.2.4	2020.2.5	2020.2.6	2020.2.7	2020.2.8	2020.2.9	2020.2.10
C (*$10^{5}$)	847	902	993	1121	1173	1211	1253
Date	2020.2.11	2020.2.12	2020.2.13	2020.2.14	2020.2.15	2020.2.16	2020.2.17
C (*$10^{5}$)	1294	1336	1390	1438	1481	1523	1557
Date	2020.2.18	2020.2.19	2020.2.20	2020.2.21	2020.2.22	2020.2.23	2020.2.24
C (*$10^{5}$)	1590	1617	1639	1662	1688	1714	1742
Date	2020.2.25	2020.2.26	2020.2.27
C (*$10^{5}$)	1775	1798	1821

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Figure 3 shows the trend of cumulative discussion in Table 2. Public opinion is closely related to the development of the epidemic. When COVID-19 first appeared in Hubei Province, China, there was quite limited attention and discussion about the epidemic. Since January 19, 2020, infections have been reported in other provinces, and the discussion on COVID-19 has gradually increased. By January 23, 2020, 830 confirmed cases had been reported across the country. From that day on, the epidemic broke out rapidly throughout China, and the public opinion ushered in a large-scale outbreak. The cumulative discussion quantity rose swiftly from 7600, 000 on January 22, 2020 to 2, 3800, 000 on January 23, 2020. Since then, the cumulative discussion quantity of COVID-19 has continued rising as the epidemic has continued intensifying.

Figure 3.  The cumulative discussion trend of COVID-19.

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The whole public opinion can be divided into two major phases: the partial hot discussion phase from December 31, 2019 to January 17, 2020 and the intense outbreak phase from January 17, 2020 on. Each major phase also included several minor stages. In the partial hot discussion phase, the development of public opinions could be divided into 3 small stages: the first stage, from December 31, 2019 to January 8, 2020, had a linear growth and stabilized later; the second stage, from January 8, 2020 to January 14, 2020, broke out in the rapid growth on January 9, 2020 and then increased slowly; and the third short stage, from January 15, 2020 to January 17, 2020, kept a relatively high speed of growth. The phase of intense explosion could also be divided into four small stages: from January 17, 2020 to January 22, 2020 in the first stage, the popularity of public opinion grew at a faster rate than the whole partial hot discussion phase; after the explosion on January 22, 2020 that entered the second stage, the speed slowed down but still grew at a higher rate than the first stage; after a smaller acceleration in January 31, 2020, the public opinion entered the third stage, which first has a lower speed than the second stage but then has a great increase on February 7, 2020 that entered the fourth stage, from February 7, 2020 until now, had a linear growth.

The division of the public opinion of COVID-19 helps us understand the trend caused by the entire epidemic hot topics. For the two large stages and seven small stages, Table 3 gives the urgent hot topics that caused the key time points. The urgent hot topics lead to a wide range of people's attention and reflection, which generated an explosion of discussion quantity.

Table 3.  Some urgent public events for COVID-19 in China.

Date	Urgent hot topics
2019.12.31	#Unexplained pneumonia found in Wuhan#
2019.1.9	#The pathogen of unexplained pneumonia in Wuhan is a novel coronavirus#
2019.1.15	#Wuhan pneumonia does not rule out the possibility of limited human-to-human transmission#
2019.1.18	#5 rumors of viral pneumonia in Wuhan#
2019.1.23	#Wuhan Sealed off#
2020.2.1	#Shuanghuanglian can inhibit the COVID-19#
2020.2.7	#Doctor Wenliang Li passed away#

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4.   Multiple-information susceptible-discussing-immune model (M-SDI)

The propagation of an event like COVID-19 on Sina-microblog accompanied by the post of multiple information within multiple topics is normal behavior. In order to more clearly show the propagation process of the event, a schematic diagram is shown in Figure 4 Taking the propagation of three Weibos under three topics as an example, the user's overall state of integrated information propagation is given.

Figure 4.  A schematic diagram for COVID-19 propagation by multiple related information.

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Discussing is a kind of behavior that reflects users' participation in information propagation, which includes posting a new Weibo (like Twit in Twitter), forwarding that or giving some comments. The Weibos posted by original post owners, such as the red nodes, and the Weibo can be discussed separately by single spreaders with interest in which users can participate in the discussion about the outbreaks, such as the black nodes. Especially, some co-spreaders between different topics or different Weibos discuss the related information successively they contacted because of the correlation about the event, such as the green nodes. Of course, there will also be many users who contact information choose to be silent (un-spread node) because they do not want to discuss in the COVID-19 event, such as the yellow node. In real-world, the number of topics and Weibos cannot be clearly calculated.

The discussion quantity of the whole COVID-19 is composed of many topics with multiple Weibos. Different from the traditional public hot events, the outbreak is causing great public concern. With the continuous development of the COVID-19, there is a high level of repetition in the public discussion on different topics. In addition to the public's repeated reading on different topics of the outbreak, users will also make subjective decisions on whether or not to discuss each Weibo in the topic. As discussion is a measure of information dissemination, in this paper, we build the multiple-information susceptible-discussing-immune (M-SDI) dynamics model with considering the "re-discussing" on the impact of public opinion propagation.

The propagation dynamics model based on discussion quantity of COVID-19 constructed in this paper is shown in Figure 5. Here, we only consider the accessible population in the process of information propagation, and only pay attention to the information diffusion caused by users' discussing behavior. It is assumed that all users that can be contacted in the whole process of the event developing are in a closed environment, and the total number of users (N) remains unchanged. At any time, each individual in the crowd may be in one of the following three states: the susceptible state (S), the discussing state (D) and the immune state (I), where the D state is consisted of many topics related to the COVID-19.

Figure 5.  A schematic diagram to illustrate multiple information spreading in the population with three different states: susceptible ($S$), discussing ($D$) and immune ($I$).

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The susceptible users can contact one Weibo of one topic with an average exposure rate $\beta$ and discuss it with the discussion probability $p$ to become discussing users, those who keep silence in the event and go straight to the immune state are with direct immunity probability $q$. The discussing users can become immune users who inactive to the event with an average inactive rate $\alpha$, with $1/\alpha$ being the average duration where a D-user remains active in contacting.

The core of our model is to study the role of repeated discussing through exposures to different Weibos in different topics about COVID-19. Hence, we use the parameter $\theta$ to describe the "re-discussing" probability for a discussing user who can return a new round of susceptible state of COVID-19.

In particular, each user may have a unique state, that is, at the same time, each user can be only one of the susceptible, discussing or immune states. We obtain the following M-SDI dynamics model:

where $' = d/dt$ is the derivative with respect to $t$. The behavior transformation and state transition of the masses can also be interpreted as follow:

Discussing: Since an active discussing user will contact an average number of $\beta N$ users per time and the probability of a contacted user is a susceptible user is $S(t)/N$, among which $p\beta N$ will choose to discuss the Weibo subjectively. Hence, the number of new discussing users is $p\beta N(S(t)/N)D(t) = p\beta S(t)D(t)$. Direct immune: Some susceptible users will not participate into discussing and enter the immune state directly because they want to keep silence in the event, and the number of new discussing users is $q\beta S(t)D(t)$. Accordingly, there are still $(1-p-q)\beta S(t)D(t)$ users who have not experienced state transition. They may simply be not interested in the Weibo they have contacted and will remain in a susceptible state waiting for the next Weibo about COVID-19. Timeout immune: The average number of inactive users will be $\alpha D(t)$ per time, among which $\theta\alpha D(t)$ will back to the susceptible state where exposures to another Weibo within same topic or with other topics can start a new round of discussing, and $(1-\theta)\alpha D(t)$ will go to the immune state directly out of an active period.

The Sina-microblog provides a piece of important information directly is the number of cumulative discussing population within a topic about COVID-19, and we calculate the sum of the whole event shown in Table 3, given by

The corresponding differential equation can be expressed as:

Considering the initial condition: ${D_0 = C_0}$, $I_0 = 0$ and $S_0 = N-D_0$. From Eqs.4.3 and Eqs.4.5 it follows $I(t)$ and $C(t)$ are increasing since $I'(t) = q\beta S(t)D(t)+(1-\theta)\alpha D(t) > 0$, $C'(t) = p\beta S(t)D(t) > 0$, therefore the final states are $I_{\infty} = \lim \limits_{t \to \infty}I(t) < N$, $C_{\infty} = \lim \limits_{t \to \infty}C(t) < N$, $D(t)$ tends to 0 ($F_{\infty} = 0$) and $S_{\infty} = N-I_{\infty}$. Here $C_{\infty}$ is the final size of the COVID-19 discussing.

Public opinion discussion reproduction ratio $\Re_0$:

We define the reproduction ratio $\Re_0(t)$ to describe the outbreak of public opinion at each time $t$. The outbreak of discussion on COVID-19 at time $t$ is given by $D'(t) = p\beta S(t)D(t)-\alpha D(t) > 0$, and the population will never take off since $D'(t) = p\beta S(t)D(t)-\alpha D(t) < 0$. Then we deduce

as the discussion reproduction ratio. The $\Re_0(t)$ denotes the number of D-population generated by topics about COVID-19 during an active period, which is determined by the average exposures rate $\beta$, the average inactive rate $\alpha$, the discussing probability $p$ and the susceptible users $S(t)$. When $\Re_0(t) < 1$ the D-population of the event will decline which implies the propagation can never take off. And when $\Re_0(t) > 1$, it means the D-population grows exponentially initially.

5.   Numerical experiment and discussing

We have divided the development of COVID-19 information dissemination into several stages as shown in Figure 3 which are affected by some urgent hot topics shown in Table 2. Although we cannot control the occurrence of emergency incidents, it is very important that, in each period of a stage, we can predict the trend of public opinion based on the existing data before the emergency comes.

To use our M-SDI model to explore some distinctions of qualitative behaviors for prediction, we use the LS method to estimate the model parameters and the initial susceptible population. The vector can be set as $\Theta = (\beta, p, q, \alpha, \theta, S_0)$, and the corresponding numerical calculation based on the parameter vector for $C(t)$ is denoted by $f_{C}(k, \Theta)$. The LS error function

is used in our calculation, where $C_k$ denotes the actual cumulative number of discussions given in Table 2, and $k = 0, 1, 2...$ is the sampling time, once a day here. In order to predict the public opinion trend at various stages earlier, we estimate the parameters of our M-SDI model with at least 3-4 days' data. In particular, we increase the sampling frequency when 3-4 sampling points cannot meet the parameters estimating conditions. We use DEDiscover software to solve this LS problem.

Figure 6 gives the numerical experiment results for prediction at each phase. The partial hot discussion phase from December 31, 2019 to January 17, 2020 has the number of cumulative discussion quantity in the order of one hundred thousand as shown in Figure 6(a)-6(c), and the intense outbreak phase from January 17, 2020 until now is nearly tens of millions shown in Figure 6(d)-6(g), where the red star denotes the actual cumulative discussion quantity we use to estimate the parameters for prediction, the pink circle denotes the actual cumulative discussion quantity we want to predict, and the blue line denotes the predicted results.

Figure 6.  The prediction of discussion quantity of COVID-19.

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At the first partial hot discussion phase, the topic #Unexplained pneumonia found in Wuhan# attracted public attention and the discussion quantity of COVID-19 began to increase. We predict the public opinion trend of COVID-19 with the data from December 31, 2019 to January 3, 2020 and it achieves a good data fitting with the actual data until January 7, 2020, as shown in Figure 6(a1). Thus, we increase the data to January 7, 2020 and predict again, fortunately, we get a satisfactory result until the end of this stage, as shown in Figure 6(a2). After the second parameter estimation, the first stage ends quickly since the topic #The pathogen of unexplained pneumonia in Wuhan is a novel coronavirus# exploded on January 9, 2020. We use three days$'$ data until January 10, 2020 to realize the third prediction, as shown in Figure 6(b1), and have the next three days$'$ good data fitting. The fourth prediction shown in Figure 6(b2) is not meaningful because the stage finished after this prediction. Similarly, there is a turning point in the third stage since the topic #Wuhan pneumonia does not rule out the possibility of limited human-to-human transmission# exploded on January 15, 2020, our M-SDI model also has a good result although this period is short, as shown in Figure 6(c1)-(c2).

The second intense outbreak phase is the most important period in COVID-19 public opinion propagation. The first stage only existed six days with the evoke of #rumors of viral pneumonia in Wuhan# in January 18, 2020. During this stage, our M-SDI model use only three days' data until January 19, 2020 to realize a good prediction until the end of this stage, as shown in Figure 6(d1). The second prediction in this intense outbreak phase also has no use (as shown in Figure 6(d2))with the outbreak of #Wuhan Sealed off# on January 23, 2020. This is the topic that has caused the most public opinion so far and the public opinion with different topics has continued until now. We use the data between January 22, 2020 and January 24, 2020 to estimate the parameters and predict the trend of public opinion of the next four days, as shown in Figure 6(e1). In addition, we increase the data until January 28, 2020 to predict the rest of the public opinion trend in this stage, as shown in Figure 6(e2). With two prediction, our M-SDI model can well predict most of the data in this important period. We use the data between January 31, 2020 and February 2, 2020 to realize a good prediction until the end of this stage, as shown in Figure 6(f1). Then we increase the data until February 5, 2020 to predict the rest of the public opinion trend in this stage, as shown in Figure 6(f2). This stage ends since the topic #Doctor Wenliang Li passed away# exploded on February 7, 2020, then we use the data between February 6, 2020 and February 8, 2020 to realize a good prediction until the end of this stage, as shown in Figure 6(g1). In addition, we increase the data until February 11, 2020 to predict the rest of the public opinion trend in this stage, and we can also have a good data fitting results as shown in Figure 6(g2).

Figure 7 shows the whole prediction of discussion quantity for COVID-19, where the red star denotes the actual number of cumulative discussion quantity and the blue triangle denotes the predicted results with our M-SDI model. At partial hot discussion phase, we can make a good prediction of the development process at seven days which are January 4-6, 8, 11-13, 17, 2020. And at the intense outbreak phase, we have a good prediction at eleven days which are January 20-22, 25-31, February 3-6, 9-now, 2020. It can be concluded that, without the occurrence of emergency incidents, our M-SDI model can well predict the trend of public opinion based on the existing data for the whole COVID-19 public hot events.

Figure 7.  The whole prediction of discussion quantity of COVID-19.

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From data fitting, more public opinion properties can also be obtained. Table 4 gives the results of estimated parameters about the influencing factors according to different time periods. From the results of parameter estimation, it can be seen that at the early stage of partial hot discussion phase (Figure 6(a)), although there are many susceptible users exposed, they keep silence to the topics about the novel coronavirus, so the average probability of entering the discussion state $\it p$ after exposure is small, and the probability of directly entering the immune state $\it q$ is large, but once the user enters the discussion state, it will be active for a long time. In the next two stages (Figure 6(b), (c)), the parameter $\it p$ increased and the cumulative number of discussions continued to increase, but there was no sharp outbreak.

Table 4.  Parameter results.

	$\beta$	$\it p$	$\it q$	$\alpha$	$\theta$	$S_0$
Figure 6(a1)	0.1118	0.0082	0.6604	$1.3443\times{10^{-6}}$	0.8016	$125.9721\times{10^5}$
Figure 6(a2)	0.3078	0.0268	0.4592	$2.1700\times{10^{-9}}$	0.2390	$14.9323\times{10^5}$
Figure 6(b1)	0.0257	0.4352	0.0068	1.2132	0.9997	$16.0828\times{10^5}$
Figure 6(b2)	0.9032	0.0481	0.6979	0.2236	0.9867	$4.1934\times{10^5}$
Figure 6(c1)	0.0045	0.1619	0.0113	0.6268	0.9972	$181.2324\times{10^5}$
Figure 6(c2)	0.0155	0.3977	0.9945	0.4330	0.0036	$19.6208\times{10^5}$
Figure 6(d1)	0.0346	0.0275	$4.0345\times{10^{-4}}$	$1.0443\times{10^{-5}}$	0.4732	$648.2643\times{10^5}$
Figure 6(d2)	0.0110	0.0042	$4.3398\times{10^{-6}}$	$2.3233\times{10^{-5}}$	0.9729	$15567\times{10^5}$
Figure 6(e1)	0.0432	0.1485	0.0956	0.4879	0.9808	$307.3187\times{10^5}$
Figure 6(e2)	0.4196	0.5003	0.1059	0.8724	0.9337	$94.0182\times{10^5}$
Figure 6(f1)	0.0020	0.2662	0.1001	0.6349	0.7655	$198.4130\times{10^5}$
Figure 6(f2)	0.1086	0.7769	$1.2098\times{10^{-13}}$	0.0897	1.0000	$8.9430\times{10^5}$
Figure 6(g1)	0.0047	0.1183	0.0441	1.5000	0.9937	$10.0017\times{10^5}$
Figure 6(g2)	0.2737	0.4832	0.4094	0.1000	0.9925	$116.2541\times{10^5}$

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Entering the early stage of intense outbreak phase (Figure 6(d)), the probability of direct immune $\it q$ after contacting the information has been greatly reduced, indicating that most users participate in the discussion, and the active time 1/$\alpha$ has increased, leading that public opinion enter a rapid outbreak phase. Then in the second stage (Figure 6(e)), the parameter $\it p$ is higher than the previous stage and the parameter $\theta$ has maintained a high value nearly 1, which indicates that users participate in the discussion with a high probability and they will enter susceptible state of another information with a high probability, therefore, public opinion continues to spark a trend in this stage. At the sixth stage (Figure 6(f)), the parameter $\it p$ is higher than the previous stage, which indicates that users participate in the discussion with a high probability. Therefore, public opinion continues to explode in this stage. At the last stage, (Figure 6(g)), with the development of the COVID-19, the parameter p reduced and the active time 1/$\alpha$ has decreased. Hence, public opinion about the COVID-19 will grow steadily.

Throughout the entire process, the important parameter $\theta$ remains at a high value in most stages, indicating that the public users will participate in the discussion of another Weibo or topic with a high probability after participating in the discussion of one Weibo or topic during the develop of COVID-19. Hence, the probability of repeated discussions is at a high level.

Throughout the entire public opinion development process of COVID-19, Figure 8 gives the prediction results in the future which uses the entire data at the intense outbreak phase and Table 5 shows some important values of parameter estimation. Unfortunately, with the development of the epidemic, Figure 8 shows that the public opinion will continue to erupt in a long time.

Figure 8.  Prediction results in the future.

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Table 5.  Some important values of parameter estimation.

Name	Estimated Value	Standard Error	CI Low Bound	CI High Bound	p-value	t-statistic	Min	Max
$S_0$(*$10^5$)	168.8749	8.7633	151.1021	186.6476	$1.4913\times{10^{-20}}$	19.2707	1.0000	$2.0000\times{10^4}$
$\alpha$	0.9792	0.5558	-0.1481	2.1064	0.0866	1.7617	0.0000	1.50000
$\beta$	0.0179	0.0049	0.0080	0.0278	$7.8418\times{10^{-4}}$	3.6681	0.0000	1.0000
$\it p$	0.5756	0.1799	0.2107	0.9405	0.0029	3.1990	0.0000	1.0000
$\it q$	0.0017	0.0318	-0.0628	0.0661	0.9588	0.0520	0.0000	1.0000
$\theta$	0.9776	0.0660	0.8439	1.1114	$6.7306\times{10^{-17}}$	14.8202	0.0000	1.0000

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In addition, Table 6 gives the results of the reproduction ratio $\Re_{0}$ at each time. When $\Re_{0} >1$ on a certain day, it means that public opinion will continue to explode. When $\Re_{0} <1$, it means the D-population of the event will decline. The results show that in the early stage of COVID-19, it has the greatest reproduction ratio $\Re_{0} = 1.7769$ and breaks out quickly. With the development of the epidemic, $\Re_{0}$ gradually decreases and stabilizes around 0.97, which indicates that in the future, the information on COVID-19 will continue to erupt slowly until it stabilizes if there is no violent information outbreak, which verifies the conclusion of Figure 8.

Table 6.  The results of the public opinion discussion reproduction ratio $\Re_{0}$.

Data	2019.12.31	2020.1.1	2020.1.2	2020.1.3	2020.1.4	2020.1.5
$\Re_{0}$	1.7769	1.7526	1.7042	1.6171	1.4849	1.3279
Data	2020.1.6	2020.1.7	2020.1.8	2020.1.9	2020.1.10	2020.1.11
$\Re_{0}$	1.1878	1.0905	1.0340	1.0044	0.9895	0.9821
Data	2020.1.12	2020.1.13	2020.1.14	2020.1.15	2020.1.16	2020.1.17
$\Re_{0}$	0.9785	0.9766	0.9758	0.9753	0.9750	0.9749
Data	2020.1.18	2020.1.19	2020.1.20	2020.1.21	2020.1.22	2020.1.23
$\Re_{0}$	0.9748	0.9748	0.9747	0.9747	0.9748	0.9747
Data	2020.1.24	2020.1.25	2020.1.26	2020.1.27	2020.1.28	2020.1.29
$\Re_{0}$	0.9747	0.9747	0.9747	0.9747	0.9747	0.9747
Data	2020.1.30	2020.1.31	2020.2.1	2020.2.2	2020.2.3	2020.2.4
$\Re_{0}$	0.9747	0.9747	0.9747	0.9747	0.9747	0.9747
Data	2020.2.5	2020.2.6	2020.2.7	2020.2.8	2020.2.9	2020.2.10
$\Re_{0}$	0.9748	0.9748	0.9748	0.9747	0.9747	0.9746
Data	2020.2.11	2020.2.12	2020.2.13	2020.2.14	2020.2.15	2020.2.16
$\Re_{0}$	0.9746	0.9747	0.9747	0.9748	0.9748	0.9748
Data	2020.2.17	2020.2.18	2020.2.19	2020.2.20	2020.2.21	2020.2.22
$\Re_{0}$	0.9748	0.9748	0.9747	0.9747	0.9747	0.9747
Data	2020.2.23	2020.2.24	2020.2.25	2020.2.26	2020.2.27
$\Re_{0}$	0.9747	0.9747	0.9747	0.9747	0.9747

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6.   Conclusion

In this paper, we proposed a multiple-information susceptible-discussing-immune (M-SDI) model based on the quantities of public discussions in Chinese Sina-microblog. Our model considers the particular feature that users are likely to re-enter the susceptible (to a news item) state of related information after discussing a certain piece of information. Using this model, we analyzed the public opinion data on the COVID-19 in Chinese Sina-microblog and stratified events development into different stages according to the disease outbreak development. In each stage, we used a small amount of data for parameter estimation and then used the parameterized model for trend prediction which agreed with the real data well until the next event occurred. We attempted to give our prediction on trend in the near future using all the data available until February 27, 2020, so the usefulness of this predictive model can be tested in the coming days.

To our best knowledge, there is no appropriate model framework that can be used to analyze multiple-information propagation during a major public health emergency. Our work fills the gap and we have shown that our proposed multiple-information susceptible-discussing-immune (M-SDI) model, equipped with early data about news item users can faithfully describe the propagation mechanism of major news items in Chinese social networks during a public health emergency. We hope this model framework provides an important technical tool to predict evolution of public opinions, and thus may provide insights how to communicate public health strategies effectively during a public health crisis including the on-going COVID-19 outbreak.

Acknowledgments

The work was supported by the National Natural Science Foundation of China (Grant numbers: 61801440), the Natural Science and Engineering Research Council of Canada, the Canada Research Chair Program (JWu), the Fundamental Research Funds for the Central Universities and the High-quality and Cutting-edge Disciplines Construction Project for Universities in Beijing (Internet Information, Communication University of China).

Conflict of interest

The authors declare no conflict of interest.