Data, model and realistic simulations

Our big data of empirical mobility tracks is based on 7-day 4G communication records between base stations and mobile phones served by one of the three major service providers between 22^nd and 28^th May 2017 in Shijiazhuang, a city in northern China, and a dataset without the influence of the pandemic in terms of both central intervention and public awareness. There are M = 11594 base stations throughout the city, and the position of an individual is recorded as the location of the nearest base station as long as his/her mobile phones communicate with the base station in 4G. As some phone applications constantly exchange data with back-end servers, the position of individuals can be recorded up to a high frequency of every second.

The original data include records from roughly 3 million users out of a total population of 11 millions in the city. To obtain a dataset of valid mobility tracks from active users, we have implemented strict rules to exclude users who do not move at all and those whose data are largely incomplete. Finally, we single out N = 702, 477 valid mobility tracks for simulations (see Method for details, and S1 Fig for the statistics of the dataset). As co-location visits by users is crucial for transmission of virus [33], we need to identify meaningful stops in a user’s mobility track. We first divide the whole period of the dataset into time windows of 15 minutes as in [34], and consider that a user stops in a location if he/she stays there continuously or discontinuously for 10 minutes or more within the time window. Otherwise, if the user did not stay in the same location for more than 10 minutes, we identify the data point as “moving”. A co-location visit is defined to occur when two individuals stop in the same location and the same time window. Regarding the potential bias of the data, first of all, the data we have is obtained from one of the largest companies among a few major cell phone service providers in China, and cover users from every district in Shijiazhuang city. Although users have different preferences in selecting cell phone companies, bias on the data due to their choice should be small, and hence the original sample of users in the data should be close to a random sample of the whole population in the city. Secondly, as we only take into account users who have continuous mobility records within the week, some users with incomplete mobility records are removed from our data analyses. This criterion may tend to remove senior or young users who do not constantly switch on and connect their phones to the 4G service. However, in order to reduce this bias, we have set the threshold of mobility below which to be defined as elderly, such that the distribution of the inferred age group of users is consistent with that in the census data of the city (see Materials and methods).

We follow the formula underlying the COVID-19 Essential Supplies Forecasting Tools (ESFT) introduced by the World Health Organization (WHO) [36], such that the reproduction number R₀ is given by (1) where D is the infectious period; M is the average number of co-location visits with the others per individual per unit time (e.g. day); γ is the fraction of co-location visits which lead to contacts, i.e. some co-location visits do not lead to contacts, for instance, users with their mobile phones connected to the same base station do not necessary imply a contact, and γM is the number of co-location contacts; and β is the probability of infection per co-location contact. In our simulations, we adopted R₀ = 7 for the Omicron variant of COVID-19 [35], an infectious period D = 7 days [36] since we have assumed that the incubation period of Omicron lasts for 1.7 days [37] and our dataset spans only for 7 days, and finally an average of M = 568 co-location visits with the others by a single individual per day from our empirical data. In this case, one can estimate the quantity γβ ≈ 0.002, which is the probability of infection per co-location contact with the others in a single time window.

By adopting the above model, we study the initial stage of the silent transmission of COVID-19 initiated from 0.01% (i.e. 70 people) of the population (see S2 Fig for the results with fewer initial spreaders). All citizens then move in the city according to their real mobility tracks. We assume that infections start with an incubation period of 1.7 days (see S4 Fig for the results with a longer incubation period), and afterwards the infected individuals would be able to infect others [37]. If a susceptible individual stays at the same location in the same time window (i.e. a co-location visit) with an infected individual passed his/her incubation period, the susceptible may be infected with a probability γβ = 0.002 (see S3 Fig for the results of smaller infection probability). We remark that the choice of γβ would mainly influence transmission speed instead of the detailed transmission dynamics, hence the main goal of the present study from the present study would be less dependent on γβ.

Since there may be more than one infected individual at a location, if we denote the number of infected individuals who have passed their incubation period at a location α in the time window at time t to be n_α(t), then the probability for a susceptible individual to get infected at α at time t is (2) Even if an individual stays in the same location for multiple consecutive time windows, the number of infected individuals may change as time evolves, and the probability for this individual to get infected in a specific time window is given by Eq (2) if he/she remains un-infected before the time window. Thus, the real mobility track of individuals determines whether they are in contact with the infected, who can be a stranger in malls, a colleague at the workplace, or a family member at home (see Method and later discussions for the inference of individual professions).

In our work, we analyze the 7-day mobility data of 700,000 cell phone users, finding that the number of people with co-location with a user is 568. Given the R₀ of Omicron is 7, we can obtain the infection probability β* (i.e. γβ) of the virus (see Eq (1)). According to the census, the size of most family in Shijiazhuang is smaller than 7, so we assume that the number of family members for each family is at most 6. Assuming that the R₀ is also 7 at home, the infection probability β* would be roughly 100 times larger than that in outdoor as the number of people in contact at home is roughly 100 times smaller than that in outdoor. In fact, considering that people usually wear masks outdoor but do not wear masks at home, R₀ at home may be even larger, and thus in one of our major scenarios of simulations, we made this assumption that the infection probability at home is 100 times larger than outdoors, leading to γβ = 0.2 at home. Nevertheless, we also understand that this is only an assumption, and therefore we also examine in S5 and S6 Figs the case with other γβ at home, and the results show that our main findings are still valid. As our data span only for one week, which is shorter than the time needed for recovery from COVID-19, we do not include recovery. We also assume that most infected individuals do not show significant symptoms in a week and the virus spreads silently. This assumption may be more valid for Omicron, since it may lead to milder or even no symptoms compared to other COVID-19 variants [38]. Hence, the mobility behavior of citizens remains un-intervened as they are unaware of the silent transmissions. This makes our dataset suitable since it recorded the mobility behavior in 2017 without the influence of the pandemic, and thus our study is unique since most other studies used only macroscopic datasets during the pandemic.

We first illustrate how our big data of high frequency mobility tracks can lead to simulations of COVID-19 transmission with an extent of completeness and realism not attained in existing studies. As an example, we show in Fig 1 two individuals who live far away from each other but co-visit some locations at the same time in a day such that silent transmissions may occur between them. Their spatial mobility tracks with various visited locations are shown in Fig 1A, where both follow a routine schedule like most of us as we can see from their sequence of visited locations in Fig 1B. In this specific day, these two individuals left home in the morning, and then went to work at the same location, so they had two periods of co-location visits i.e. one in the morning and the other in the afternoon at the work place. After work, they went to the same venue for a concert, which led to their third co-location visit in that day. According to our adopted spreading model, if one of them has been infected with COVID-19 before the day, the other individual would have a probability of γβ to get infected in each co-location visit in each time window.

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Fig 1. Exemplar high-resolution city-wise human mobility tracks and potential silent transmission of COVID-19 via co-location visits.

(A) The map and the distribution of population in Shijiazhuang, and the city center is enlarged and the exemplar mobility tracks from two individuals are shown on the right. (B) Their corresponding sequence of visited locations, numbered according to the location labels in the enlarged map, with the category of each location shown. Blocks in gray correspond to the period when the individuals are “moving” Their co-location visits, i.e. they stop at the same location in the same time window, are marked by dashed squares. The icons used in this figure were obtained or modified from open-source resources in Openclipart (https://openclipart.org/). The map was drawn based on open-source shape file with License Creative Commons BY 40 (CC BY 4.0) from OpenStreetMap (https://www.openstreetmap.org/).

https://doi.org/10.1371/journal.pcbi.1011083.g001

Daily periodic transmission dynamics

To reveal details of the transmission dynamics difficult to observe without our high-frequency empirical mobility tracks, we show in Fig 2A the number of new infections ΔI(t) in the city as a function of time t at a 15-minute interval. According to our analyses, most mobility tracks follow a regular pattern, which are mostly found outside home at different locations in the daytime and stationary at home in the night-time. In general, individuals are more likely to have co-location visits with others and get infected when they visit locations outside home, and less likely to get infected at home, despite the infection rate at home is higher. It is because they came into contact with many others outside home, but only a few family members at home. Therefore, one can observe a significant periodic pattern in ΔI(t) in Fig 2A, of which peaks and troughs correspond to daytime and night-time respectively. Interestingly, small troughs are found in between mornings and afternoons, which may correspond to individuals going home for lunch or rest at lunch time. All these results suggest that staying home does help suppressing the silent transmissions of COVID-19, even for a short time like lunch time.

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Fig 2. The spatiotemporal patterns of city-wise COVID-19 infection.

(A) The number of new infections ΔI(t) in the city as a function of time t at a 15-minute interval, given 70 randomly selected initial spreaders, averaged over 1000 realizations. A significant periodic pattern is observed, which is caused by the periodic human mobility behavior. Inset: The corresponding fraction of infected population, i.e. I(t)/N. (B) The distribution of the initial and the final infected population over the districts, i.e. I_d(0)/I(0) and I_d(T)/I(T) respectively; districts are numbered as shown in the map in C. (C) The evolution of the daily spatial pattern of the infected population in the city; the number of infected population in a location is represented by the color of the dot. The map was drawn based on open-source shape file with License Creative Commons BY 40 (CC BY 4.0) from OpenStreetMap (https://www.openstreetmap.org/).

https://doi.org/10.1371/journal.pcbi.1011083.g002

In the inset of Fig 2A, we show the fraction of infected population as a function of time t, i.e. I(t)/N, where is the total number of infections at time t. Although there are only 70 initial spreaders, a city-wise infection can occur in a week. These transmissions may seem much faster than those in reality; this is because in reality COVID-19 transmissions always come with a high anti-pandemic awareness, preventive and intervention measures, while in our simulations we assume silent transmissions without any interventions. Hence, our results can also serve as a benchmark to demonstrate how COVID-19 spreads given no anti-pandemic awareness nor interventions. However, the fast transmissions observed in our simulations are also dependent on our inferred infection probability γβ, which may be different from that in reality. Nevertheless, our following major results which compare infections across age groups and professions, locations and districts, etc. are relative to each other and less dependent on the pace of transmissions and thus our estimate of γβ.

We then go on to examine how transmissions occur in different districts of the city. Such analysis would be difficult even in reality by contact tracing since it is often hard to determine how an individual gets infected [7], but would be straightforward in our case by agent-based simulations overlaying a big data of empirical mobility tracks. We first denote I_d(t) as the number of infected individuals at time t who live in district d, with d denoting one of the 22 districts in the city (see S1 Table for the information of individual districts). We show in Fig 2B the distribution of the initial and the final infected population over the districts, i.e. I_d(0)/I(0) and I_d(T)/I(T) respectively with T denoting the ending time of the dataset. As the initial infected individuals are randomly selected, their presence should be proportional to the population of a district. As we can see, the final fraction of infected population in a district is not proportional to its initial fraction, i.e. , since the infected individuals move across different districts in the city. Interestingly, districts with a large share of initial infected population tend to have an even larger share at last. These districts are mainly regions in the city center with a high population density, and they are also business centers where citizens from other districts come to work or gather in the daytime, causing cross infections. Interestingly, the districts with a small share of initial infected individuals, on the contrary, tend to have an even smaller share of the final infected population. It is because these districts are mostly suburban or rural areas, and their residents are less likely to visit city centers and residents in other areas are also less likely to visit them, which reduces transmissions. In addition, the small population density in these areas may also reduce COVID-19 transmissions since residents have less frequent contacts with others. We show in Fig 2C the evolution of the spatial pattern of the infected population in the city, which further supports our conjecture that the infections are highly clustered in the city center or regions with a high population density. The results suggest that visiting city centers and meeting strangers from other areas of the city may lead to a high risk of infection.

Profession- and location-dependent transmissions

Based on the nature of the location of base stations, one can identify the nature of the locations visited by users in their mobility tracks. According to their nature, we classify locations into 15 location categories such as malls, schools, etc. With this information, we can infer the profession of individual users (see Method for details) and study the relationship between professions and the transmission of COVID-19.

In Fig 3A, we show how the number of newly infected individuals with different inferred professions increases with time t, i.e. ΔI_p(t) with the subscript denoting inferred profession p. An immediate observation is that the periodic pattern still exists for most professions, but the number of infected individuals is largely different across professions as they have a different population size. The top two infected professions are industrial and corporate workers and freelancers, which are also the two professions with the largest population size. To better compare the infection dynamics across professions, we show in the inset of Fig 3A the fraction ΔI_p(t)/I_p(T), i.e. the fraction of infected population of profession p who get infected at time t; this allows us to compare the periodic pattern of new infections across professions with vastly different population size. One can see that most professions follow the same periodic infection patterns, except retirees who are more likely to be infected in the night-time, possibly caused by their family members who come back home after work.

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Fig 3. Infected professions and locations.

(A) The number of newly infected individuals of different professions p as a function of time t, i.e. ΔI_p(t). Inset: the fraction of infected population from profession p who get infected at time t, i.e. ΔI_p(t)/I_p(T), averaged over 1000 realizations. Periodic patterns still exist for different professions, but their infected population is largely different. (B) The number of transmissions in locations of different location category l as a function of time t, i.e. ΔI_l(t). Inset: the fraction of transmissions in location category l which occur at time t, i.e. ΔI_l(t)/I_l(T). (C) Upper panel: the distribution of population over professions (orange bars), i.e. N_p/N, which is proportional to the initial distribution of the infected population over professions I_p(0)/I(0), and the corresponding final infected distribution (green bars), i.e. I_p(T)/I(T); lower panel: the fraction of final infected individuals normalized by the population size in each profession, i.e. I_p(T)/N_p. (D) Upper panel: the distribution of locations over location categories, i.e. M_l/M and the final distribution of transmissions over location categories, i.e. I_l(T)/I(T); lower panel: the average number of transmissions in a single location of each location category, i.e. I_l(T)/M_l.

https://doi.org/10.1371/journal.pcbi.1011083.g003

To compare the likelihood of infection by profession, we show in the upper panel of Fig 3C the distribution of population over professions (orange bars), i.e. N_p/N, which is proportional to the initial distribution of the infected population over professions I_p(0)/I(0) since the initial infected group is randomly selected; we also show the corresponding final infected distribution (green bars), i.e. I_p(T)/I(T). In the lower panel, we show the final fraction of infected individuals normalized by the population size in each profession, i.e. I_p(T)/N_p. As we can see, despite that retirees take up a large fraction of the population as shown by the orange bars, their final share of infection is small, implying a low infection rate for them as also shown by the red bars in the lower panel. This is an interesting characteristic of the pandemic not revealed in previous studies. Nevertheless, here we assume that all the elderly are living in households with at most 6 family members, and thus transmissions in elderly homes are not considered which can greatly increase the infection rate for the elderly. Unlike retirees who are characterized with the smallest infection rate, professions with the highest infection rate include retailing, catering and hotel management. They are all service professions who are in contact with many strangers every day, and some of these strangers may come from other districts leading to long-distance silent transmissions. If these service providers are infected, they may also act like an infection hub to distribute the virus across different areas of the city, again through the strangers they.

To further understand the reason behind profession-dependent infections, we show in Fig 3B the number of transmissions in locations of different category as a function of time t, i.e. ΔI_l(t) with l denoting the category of location. This is a quantity which can be measured easily in simulations, but not empirically since transmission are difficult to be identified in reality. As we can see, on top of the periodic patterns, the largest number of transmissions occurs in malls and markets, followed by urban residential areas and corporates. The inset of Fig 3B shows the fraction of transmissions at locations in category l which occur at time t, i.e. ΔI_l(t)/I_l(T); this again allows us to compare the periodic patterns of new transmissions across location categories with vastly different number of transmissions. One can now see an obvious peak for “entertainment premises” in the last day of the simulations, which came from a massive gathering in an evening concert (see Fig 1 for the mobility tracks of two individuals who attended the concert). This shows that large gathering events do pose a high risk of large-scale transmissions.

In Fig 3D, we show in the upper panel the distribution of locations over different categories, i.e. M_l/M, where M_l corresponds to the number locations which belong to category l; the final distribution of transmissions over location categories, i.e. I_l(T)/I(T), is also shown. In the lower panel, we show the average number of transmissions in a single location of each location category, i.e. I_l(T)/M_l. The results suggest that the risk to be infected is highest in malls and markets, hotels and transportation hubs, but lowest in villages and urban residential areas, in consistent with our above findings on profession-dependent transmissions as well as our expectation that locations where people gather are likely for transmission of COVID-19. In this case, stricter intervention measures can be imposed in locations of the high-risk location categories.

Other than profession-related locations, everyone goes home and stay probably a long time there in a day, it is therefore important to examine how often transmissions occur at home. We remark that we do not associate home to any of the location categories, since we define home as the location an individual stayed the longest time over-night instead of based on the nature of the location (see Method for details). In Fig 4A, we compare how the number of transmissions inside and outside home increases with time t. As we can see, transmissions occur more frequently outside than at home. The inset of Fig 4A shows the fraction of transmissions inside and outside home which occur at time t, i.e. ΔI(t|home)/I(T|home) and ΔI(t|outside)/I(T|outside) respectively. This again enables us to compare the periodic patterns in spite of the difference in their total number of transmissions. As we can see, both fractions show a periodic pattern but are roughly out of phase, i.e. the peaks of transmissions at home are found roughly in the night-time which are also the minima for transmissions outside.

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Fig 4. Transmissions inside and outside home and their dependence on age.

(A) The number of new transmissions inside and outside home as a function of time t, averaged over 1000 realizations. Inset: the fraction of transmissions inside and outside home normalized by the total number of transmissions as a function of time t, i.e. ΔI(t|home)/I(T|home) and ΔI(t|outside)/I(T|outside) respectively. (B) The number of new infected individuals as a function of time t in different age groups, i.e. ΔI_a(t). Inset: the fraction of infections in different age groups which occur at time t, i.e. ΔI_a(t)/I_a(T). (C) The distribution of initial and final infected population across different age groups, i.e. I_a(0)/I(0) and I_a(T)/I(T) as orange and green bars respectively, and the fraction of individuals infected at home in different age groups, i.e. I_a(T|home)/I_a(T) (red bars). (D) The fraction of population infected inside and outside their home according to their professions, i.e. I_p(T|home)/I_p(T) and I_p(T|outside)/I_p(T) respectively.

https://doi.org/10.1371/journal.pcbi.1011083.g004

The dependence of infection on age groups

Based on the locations individuals visited, their inferred professions and the demographic data from the 7^th official Census of Shijiazhuang, we can further infer and classify individual users into three age groups, namely (1) under 15, (2) 15 to 60, and (3) above 60 (see Method for details). We then go on to investigate how transmissions occur within and across age groups. In particular, both hospitalization and fatality by COVID-19 increase with age, leading to immense pressure on the public healthcare systems, and it is worthwhile to examine how transmissions to the senior population can be suppressed.

In Fig 4B, we show how the number of newly infected individuals increases with time t in different age groups, i.e. ΔI_a(t) with a denoting the age group. As the largest fraction of the population falls in the second group with age between 15 and 60, it has the largest share of infected population. We further show in the inset of Fig 4B the fraction of new infections in different age groups which occur at time t, i.e. ΔI_a(t)/I_a(T). As we can see, senior population with age above 60 evolves differently from those in the other two age groups. Specifically, the senior age group tends to have a higher probability to be infected during the weekend, i.e. the 6^th and the 7^th day in our dataset, possibly because their younger infected family members stay at home for a long time or they go out with their family members during the weekend. Fig 4C further shows the distribution of initial and final infected population across different age groups, i.e. I_a(0)/I(0) and I_a(T)/I(T) respectively, which suggests that in general the senior population is less likely to be infected due to their smaller mobility. The red bars of Fig 4C also show the fraction of individuals infected at home in different age groups, i.e. I_a(T|home)/I_a(T). One can see that the senior population are much more likely to be infected at home than younger people.

The above results suggest some specific ways for the senior population to get infected, and are further supported by our profession-dependent analyses. We show in Fig 4D the fraction of population infected inside and outside their home according to their professions, i.e. I_p(T|home)/I_p(T) and I_p(T|outside)/I_p(T) respectively. Since retirees are mainly composed of the senior population, they are the only group who are more likely to be infected at home than outside. As COVID-19 impacts the senior population more severely, to reduce death toll, our results suggest that it is important to avoid the senior population to get infected at home, for instance, to impose prevention measures at home such as wearing masks or to reduce the frequency of high-risk family members visiting or staying with them during the pandemic [8].

Profession-specific and location-specific source of infection

Finally we study how the final state of infection in the city depends on the initial group of infected [39]. Intuitively, the final state depends significantly on the professions and locations of the initial infected group. The radar maps in Fig 5A and 5B show the total number of the infected population over professions until the 3^rd and the 7^th day of the simulations respectively, i.e. I_p(3^rd day) and I_p(7^th day), given that each of the initial infected group falls completely in four different professions (see S7 Fig for the results with the initial infected group in other professions). These results suggest that the distribution of infected professions on the 3^rd day can be substantially different, depending on the initially infected profession. For instance, retailing is the most infected profession given that retailers are initially infected, but less affected if the initial infected group comes from other professions. On the other hand, one can see from Fig 5B that the final distributions of the infected population initiated by different infected groups look similar, suggesting that the distributions of the infected individuals over professions become more independent of the initial infected groups as time evolves. These results imply that the professions of the initial infected population may have a short-term impact on the distribution of the infected population, but this impact reduces as the pandemic evolves, and ultimately the final state of infection may become independent of the sources.

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Fig 5. Effect of initial spreaders.

The number of the infected population over professions until (A) the 3^rd and (B) the 7^th day of the simulations respectively, i.e. I_p(3^rd day) and I_p(7^th day), given that each of the initial infected group falls completely in four different professions. Similar investigation on (C) I_l(3^rd day) and (D) I_l(7^th day) for location categories, given that the initial infection starts at locations in four different location categories.

https://doi.org/10.1371/journal.pcbi.1011083.g005

Similar results can be seen in Fig 5C and 5D when we investigate the total number of transmissions over location categories until the 3^rd and the 7^th day of the simulations respectively, i.e. I_l(3^rd day) and I_l(7^th day), given that initial infection starts at locations in four different location categories (see S8 Fig for the results where initial infection starts at other location categories). The results suggest that in the first few days, tracing the sources of infection is important as it affects the professions and locations which are shortly infected. However, in the later stage, source tracing is no longer important as the final infection state becomes independent of the sources.

Finally, we show in the S9 Fig the simulation results where transmissions through both contact and environment are considered. In this case, we first randomly select 70 individuals as the initial infected group and they spread COVID-19 via co-location contacts as in our previous simulations. We then consider four location categories for environmental transmissions, i.e. an individual who visits locations in these four categories would have a probability 0.002 to be infected on top of the probability via co-location contacts with infected individuals. In other words, visits to these locations may result in infections even if no infected individual is present in these locations in the same time window. As we can see from S9 Fig, the results of transmissions are qualitatively similar to those in Fig 5C and 5D, where one can see a high heterogeneity of infections at the early stage when the environmental spreading occurs at different location categories, but then the states of infection become similar at the later stage.

Dataset of mobility tracks

Our original data is composed of 7-day 4G communication records between base stations and mobile phones served by one of the three major service providers between 22^nd and 28^th May 2017, from close to 3 million users out of a total population of 11 millions in Shijiazhuang, a city in northern China. There are over 11500 base stations throughout the city, and the position of an individual is recorded as the location of the nearest base station as long as his/her mobile phones communicate with the base stations in 4G. As some phone applications constantly exchange data with back-end servers, the position of individuals can be recorded up to a high frequency of every second. We then divide each single day into 96 time windows, each with a duration of 15 minutes, and consider a user stops in a location if he/she stays there continuously or discontinuously for 10 minutes or more within the 15-minute time window. Otherwise, if the user does not stay in the same location for more than 10 minutes within a time window, we identify the data point as “moving”.

To identify those active users with a valid mobility track, we require the following characteristics to be present in each mobility track: (1) a location of home (see below for the inference of home position); (2) records of mobility in all 7 days; (3) a location outside home recorded in at least one time window per day; (4) at most 30 “moving” time windows among all the 96 time windows per day; (5) less than 24 time windows at home among the 60 time windows per day during the daytime which we define as the period between 6am to 9pm. Finally, 702,477 mobility tracks satisfy the above requirements and were used in our simulations.

Inference of users’ home, workplace and profession

To analyze how the virus transmits inside and outside home, we define the home location of each individual to be the location he/she stayed the longest time between 8pm to 7am the next morning during weekdays, and with at least 6 hours of stay. Since 4G communications from mobile phones sometimes switch between nearby base stations even if the phones are stationary, we substitute the overnight locations of a user which were within 250m from his/her inferred home location by his/her inferred home location, following the definition in [41]. Similarly, we define the workplace for each individual to be the location he/she stayed the longest time between 7am to 8pm on the same day during weekdays, and with at least 3 hours of stay.

Based on the workplace, we can first group users into 13 profession categories which include catering staff, village workers, university staff, transportation staff, hotel staff, urban residential workers, industrial and corporate workers, retailers, suburban workers, entertainment staff, medical practitioners, school students and civil servants. We remark that urban residential workers, suburban workers and village workers include individuals whose workplace locations are identified in urban residential areas, suburban areas and villages respectively, but the exact nature of the location is not known. On the other hand, entertainment staff include providers of entertainment and accessory services such as karaoke, hair salon, public bathrooms, car maintenance, etc. Users whose workplace cannot be identified using the above criteria are first considered as “freelancers”. Some of the freelancers are then considered as retirees as we will describe below. We also remark that although our inference of users’ home, workplace, profession and age group may not be perfect, such inference from real data would still lead to much more realistic simulations compared to agent-based simulation studies of which the properties of individual agents are all modeled.

Inference of users’ age

Based on the 7^th official Census of Shijiazhuang in 2022, we group users into three age groups, namely (1) under 15, (2) 15 to 60, and (3) above 60. To infer the age group of individual users based on their mobility tracks, we first classify users with profession “school students” as under 15. On the other hand, to identify elderly users, we calculate the daily total traveling distance and the radius of gyration for all recorded users as shown in Table 1, and for those “freelancers” with both of these measures ranked in the bottom 15% percentile, they are re-classified as “retirees” and are included in the age group with age above 60. Finally, the population in the three age groups in each district is consistent to the statistics given by the 7^th Census of Shijiazhuang.

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Table 1. The average, median, 25^th and 15^th percentile of daily total traveling distance and the radius of gyration estimated from the mobility tracks of all users.

https://doi.org/10.1371/journal.pcbi.1011083.t001

Modeling household members

Since our dataset only includes the mobility patterns of individual users without other information, to analyze transmissions at home, we have to select the household members of individual users. From the 7^th Census of Shijiazhuang in 2022, we obtain the statistics on the number of members in a household as shown in Table 2. We then randomly group individual users with the same inferred home location in households according to these statistics, with only one requirement that individuals under 15 cannot form a household by themselves.

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Table 2. The statistics of the number of members per household in Shijiazhuang based on the 7^th Census in 2022.

https://doi.org/10.1371/journal.pcbi.1011083.t002