Introduction

Much effort has been devoted to the study of human dynamics under regular and stationary situations7,9,10,11,15,16,19,23,28,30,31,32,34,37,40,45. Our quantitative understanding of human behavior under extreme conditions, such as violent conflicts5, life-threatening epidemic outbreaks3,9,10,25 and other large-scale emergencies, remains limited however. Yet, it is essential for a number of practical problems faced by emergency responders29. There is an extraordinary need, therefore, to quantitatively study human dynamics and social interactions under rapidly changing or unfamiliar conditions.

Previous studies2,24 have suggested that mobile phones can act as in situ sensors for human behavior during anomalous events, finding that the occurrence of anomalous events triggers a large spike in the communication activity of those who witnessed the event. More specifically, they found that communication spikes following emergencies are temporally and spatially localized, indicating information flow through the social networks of affected individuals becomes an important means to spread situational awareness and information to the general population.

In this work, we quantify the propagation of real-world emergency information through the contact networks of mobile phone users. We denote the group of users directly affected by an emergency by population G0, while users they contact during the timespan of the emergency that are not in G0 form the population G1. We focus here on how G1 users change their communication patterns following an emergency. To be specific, we address three questions: First, to what magnitude do G1 users change their communication behavior? Do they show the same volume spike as previously observed for G0 users2? Second, what is the origin of the behavior changes of G1 users? What is the dominant feature of these changes? Third, will a G1 user prefer to call back the G0 user, potentially offering comfort, support and seeking pertinent information? Or will they instead call forward to propagate their situational awareness to others. Intuitively we expect that G1 users were chosen for contact by the G0 users due to important relationship(s) between them and they may communicate with each other more often than with other peers even during normal days. It is therefore important for future emergency detection and intervention to know whether or not there is abnormal reciprocal communication during emergencies, compared with ordinary activity levels.

Data and events

In this paper, we use a de-identified dataset from a large mobile phone company in a European country1,4,8,14,16,20,21,27,28,33,36,37,39,42,43,44. The data consist of approximately 10 million users and four years of cell phone activity, including both voice calls and text messages. Each data entry records the user initiating the call or text (caller) and the user receiving it (callee); the cellular tower that routed the call; and the date and time when it occurred. The locations (longitude and latitude) of cellular towers are also recorded, allowing us to infer the location of callers whenever they initiate a communication. Hence, given the spatiotemporal localization of an event, these data offers a unique opportunity to quantify the social response of the affected population.

To study real events covered by this mobile phone data, we need to determine their times and locations. We study the event set identified in previous studies2, where the authors used Google local news (news.google.com) service to search for news stories covering the country and time period of the mobile phone dataset. Keywords such as ‘emergency’, ‘disaster’, ‘concert’, etc. were used to find potential news stories. Important events such as bombings, earthquakes and concerts are prominently covered in the social media. Study of these reports typically gave the precise time and the locations for these events2.

To identify the beginning and the end of an event, tstart and tstop, we adopt the following procedure2. First, we scan all calls in the event region during the day covering the event, giving the event day call volume time series (number of calls per minute) Vevent(t)2. Then, we scan calls for a number of “normal” days, those modulo one week from the event day, exploiting the weekly periodicity of V(t). These normal days' call volume time series are averaged to get 〈Vnormal〉. To smooth the time series, call volumes were binned into 10 minute intervals. The standard deviation σ(Vnormal) as a function of time is then used to compute z(t) = ΔV(t)/σ(Vnormal), where ΔV(t) = Vevent(t) − 〈Vnormal〉 is the call volume change during the event day. Finally, the interval [tstart, tstop] was the longest contiguous run of time intervals where z(t) > zthr, for some fixed cutoff zthr. To be consistent with pervious studies2, we chose zthr = 1.5 for all events.

Results

To extract the contact network between users during an event, we track all outgoing calls in order of occurrence during the event's time interval [tstart, tstop]. We therefore identified the individuals located within the event region (G0), as well as a G1 group consisting of individuals outside the event region but who receive calls from the G0 group during the event, a G2 group that receive calls from G1 and so on.

To determine how unusual the observed activities are, we compare the call volume during the event to the average call volumes of a number of “normal” days (Sec. Data and events). Since a temporal contact network can always be constructed from mobile phone dataset, even when no event occurs, it is necessary to design a proper control for normal days to make the call volumes between event day and normal days comparable.

To design a proper control, we study new “cascades” generated by the same eyewitness users G0 during the same time interval [tstart, tstop] for each normal day and create a different cascade {G0, g1, g2, …} for each normal day. Gi are for event period whereas gi are for normal period. Gi and gi share the same G0, that is by definition G0 = g0. e.g. g1 users are the users who receive cell-phone communication directly from G0 users, gi users (i > 1) are the users who receive cell-phone communication directly from gi−1 users.

The number of Gi users will typically be larger than that of gi users and Gi users may be more active than gi users, so the normal day's call volume time series, V(t|gi), must be rescaled when compared to the event day's call volume time series, V(t|Gi). For this purpose, we multiply V(t|gi) by a constant scaling factor ai,

where both integrals run over the same “calibration interval” δt and τ = 0 is the start of the selection window. For most events, we integrate over a 24-hour period two days before the event window. The factor ai was chosen such that the total number of calls during normal time periods for V(t|Gi) is approximately equal to aiV(t|gi), equalizing the normal-day time series and removing any biases due to |Gi| ≠ |gi|. This control procedure allows us to investigate call volume patterns of different user groups.

To explore the call volume patterns in different user groups, we measure the call volume change

for G0 and G1 groups as a function of time, where V(t|Gi) is the call volume in the event day and 〈aiV(t|gi)〉 is the call volume averaged over selected “normal” days.

Previous work has studied several aspects of communication patterns and found a spike in the volume of phone call activity during an emergency event2. Yet, by using the control mentioned above, we find the call volume change for different groups such as G0 and G1 exhibits different patterns in different events (Fig. 1). More specifically, we observe activity spikes in both G0 and G1 groups for three emergency events, referred to as “Jet Scare”, “Plane Crash” and “Bombing” (Fig. 1a–c). Yet in all other events, there is no volume spike for the G1 group, e.g. “Concert” (Fig. 1d). These results are consistent with previous findings2, showing that the users in the G1 group are triggered to a higher communication level, characterized by a sharp increase in call volumes, during the emergency events. Yet, it is somewhat puzzling that the call volume change of G1 users have a spike, which is instantaneous and shows virtually no delay to the spike of G0 users'. Note the spikes of G0 and G1 users are synchronous qualitatively and sensitive to the time aggregation (see Supplementary Materials). As the activity spikes of G0 users for emergency events are both temporally and spatially localized, the communication of G1 users becomes the most important means of spreading situational awareness.

Figure 1
figure 1

The temporal behavior of the call volume change for three emergency events and one non-emergency event.

(a), Jet Scare; (b), Plane Crash; (c), Bombing; (d), Concert. Call volume changes for the event are compared to the average rescaled call volume change of five corresponding normal days to compute ΔV(t|Gi). Dark blue line is for G0 users, dark red line is for G1 users. Vertical dashed line in red is the start time of the event.

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To quantify the reach of situational awareness, we focus on G1 and study their communication patterns after receiving a phone call or message from G0. As an example, we choose three G0 users (diamonds) and their related G1 users (circles) and G2 users (triangles) in the Bombing event as a sample contact network (Fig. 2a). There are three types of communication behaviors for users in G1: (1) call back to G0 user(s), which are edges in orange, (2) call forward to G2 users, edges in purple and (3) calls to other G1 user(s), edges in green. We denote these three kinds of communication behaviors with, C10, C12 and C11, respectively. We measure the contributions of these three communication modes to the total activities of G1 users, finding C11 constitutes no more than 5% of the total volume of G1 users' communicating activities (Fig. 2b). The observed low volume of C11 among G1 users during emergencies is somewhat unexpected, given the importance of triadic closure in social communications6,17. Hence, the spike observed in G1 users in Fig. 1 is mainly determined by C10 and C12.

Figure 2
figure 2

There are three kinds of communicating behaviors for G1 users.

(a), A random sample contact network during the Bombing. The G0, G1 and G2 users are in red (diamond), yellow (circle) and blue (triangle), respectively. Edges in orange, purple and green represent call back (C10), call forward (C12) and calls to other G1 users (C11), respectively. (b), Histogram demonstrating how strongly each communication pattern contributes to the total communication activity. Only ≈ 5% of V(G1)event is due to V(C11) activity for example.

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The existence of different communication modes in G1 (Fig. 2a) raises an important question: what is the temporal contribution of C10 and C12 to the observed spikes in G1 users' activities? To this end, we decompose ΔV(t|G1) into V(C10) and V(C12) by modifying the rescaling framework

for i = {0, 2}, where V1i is the call volume from G1 (g1) users to Gi (gi) users and a1i is a scaling factor modified from Eq. 1 as

In Fig. 3, we show V(C10) and V(C12) as a function of time. We find that in all three emergency events, V(C10) has evident volume spikes during the event period. And, by comparing Fig. 1 and Fig. 3, we find the peaks of V(C10) are in close temporal vicinity to those of ΔV(t|G1). Yet, for Concert (Fig. 3d), we observed no clear volume spikes. Overall, Fig. 3 demonstrates that C10, as a major contribution to the observed spikes in G1, indicating the call back actions (C10) in emergencies contribute more to the spike of ΔV(t|G1) than the call forward actions (C12). That is, G1 users prefer to interact back with G0 users rather than contacting with new users (G2), a phenomenon that limits the spreading of information. Indeed, C10 measures the reciprocal communications from G1 to G0, representing correspondence and coordination calls between social neighbors. C12, on the other hand, measures the dissemination of situational awareness, corresponding to information cascades that penetrate the underlying social network. Hence, the results in Fig. 3 indicate that during emergencies both dissemination and call-back response of emergency information are important for information flow and they together determine the magnitude of G1 users' communication spikes (Fig. 1).

Figure 3
figure 3

The time dependence of call volume V(C10) and V(C12) for three emergency events and one non-emergency event.

Solid (orange) line is call back volume V(C10), dash (purple) line is call forward volume V(C12). Vertical dash lines in red are the start and the end times of the event.

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These preceding results indicate that reciprocal communications play a dominant role in social response during emergency, raising an important question: what is the origin of the observed reciprocal correspondence? There are two possible mechanisms likely at work here. First is the heterogeneous nature of reciprocities: Social ties are characterized by different reciprocities18,22,26,35,38,41, corresponding to different likelihood of reciprocal communications upon receiving a call from others. Therefore, the large increase in reciprocal communications may represent a selection bias introduced by eyewitnesses by communicating with their social neighbors with high reciprocity. The second possible factor is a behavioral change of social neighbors after learning about the event, corresponding to coordination and providing additional information to eyewitnesses. To quantify the competition between these two factors, we measure the reciprocity of communications between any two individuals, during normal periods.

In an unweighted network, a general definition of link reciprocity R is to measure the tendency of two nodes to form mutual connections (A → B and B → A)12,26,46. Hence, R = 1 for a purely bidirectional link and R = 0 for a unidirectional one. Considering the weighted nature of contact networks13,22,41, we define the reciprocity of communications between G0 and G1 users as

where Vx→y is the number of calls from user x to user y within a given period and |·| is the absolute value. With this definition, two users have a reciprocity ranging from 0 to 1, where R = 1 corresponds to reciprocal links and R = 0 for non-reciprocal ones.

In Fig. 4, we show the reciprocity of communications averaged over all pairs of users in G0 and G1 for the four events during event periods. We find that, for Bombing, Plane Crash and Jet Scare, the average reciprocity for each emergency event shows a significant increase, deviating by approximately 1.8, 3 and 6 standard deviations from normal days, respectively. This result indicates that the observed increase in “call-back” actions from G1 to G0 during these emergency events correspond to behavioral changes in communications. If the increased call-back were entirely random, the distribution of reciprocity over the G1 population would be sufficient to explain the resulting call-back, but we do not observe this. For Concert, we observe a decrease in reciprocity comparing to normal periods, with 4.7σ below the averaged reciprocity of normal days, indicating clear distinctions between emergency and non-emergency events.

Figure 4
figure 4

Histogram for the average reciprocity (Eq.5) of communications during event period for three emergency events and one non-emergency event.

The reciprocities of communications are averaged over all observed links between G0 and G1 users for the event day and each normal day. Event day's value is in red. The final averaged value for normal day is in blue and averaged over five normal days' averaged reciprocities. The standard deviation of five normal days' averaged reciprocities are also shown as a error bar for each event.

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To test the consistency of our results, we also study reciprocity for other emergency and non-emergency events. As shown in Supplementary Materials Fig. S1, the reciprocities for Blackout and Earthquake are characterized by only modest increase, well within the range of one standard deviation, reassuring the preceding results on correlations between activity spikes in G1 (Fig. 3a in Ref. 2) and their increase in reciprocity.

Finally, to better understand the origin of the observed increase of reciprocity, we measure the contributions to G1 users' behavioral change for different demographics. More specifically, we obtained self-reported gender information, available for 88% of users and consider all communications in which gender information is available for both parties. There are four kinds of coupled pairs between G0 and G1 users: male-male (MM), male-female (MF), female-male (FM) and female-female (FF). For each event, we compute the reciprocities for the four different kinds of pairs separately. We also average the reciprocities of the MF and FM pairs as cross-gender pairs (CG) and the MM and FF pairs as same-gender pairs (SG). Interestingly, we find the collective response from different demographics is almost universal (Fig. 5). That is, for emergency events with significant increases in reciprocity (Jet Scare and Plane Crash), the reciprocities across different gender pairs are all several standard deviations larger than normal periods (Fig. 4 (a) and (b)).

Figure 5
figure 5

Gender influence on reciprocity.

Histogram for the average reciprocity of communications during three emergency events [(a) Jet Scare, (b) Plane Crash, (c) Bombing] and one non-emergency event [(d) Concert]. In (a) and (b), there is a strong change in R which is unaffected by gender. In (c) and (d), however, reciprocity does not generally change in a significant manner. Error bars denote the standard deviation.

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Discussion

Taken together, we have studied cell phone communications during anomalous events and find volume spikes in G1's communication compared to normal days in three emergencies. To uncover the possible origin of the volume spikes, we decomposed G1's communications into call-back (C10) and call-forward (C12) actions. Comparing to non-emergency events, we found that the dominant component of volume spikes is C10 for all three emergency events, indicating the need for correspondence with eyewitnesses is more critical than the dissemination of situational awareness during emergencies. We further demonstrated such communication patterns correspond to a behavioral change in G1 users that cannot be explained by reciprocity or demographics. We believe the empirical findings reported in this paper present relevant information that can be used to benchmark potential models and will play an increasingly important role as large-scale data flourish and our quantitative understanding human behavior deepens.