Colman et al. BMC Infectious Diseases (2018) 18:219 https://doi.org/10.1186/s12879-018-3117-6

RESEARCH ARTICLE Open Access The reachability of contagion in temporal contact networks: how disease latency can exploit the rhythm of human behavior Ewan Colman*, Kristen Spies and Shweta Bansal

Abstract Background: The symptoms of many infectious diseases influence their to withdraw from social activity limiting their potential to spread. Successful therefore requires the onset of infectiousness to coincide with a time when the host is socially active. Since social activity and infectiousness are both temporal phenomena, we hypothesize that diseases are most pervasive when these two processes are synchronized. Methods: We consider disease dynamics that incorporate behavioral responses that effectively shorten the infectious period of the pathogen. Using data collected from face-to-face social interactions and synthetic contact networks constructed from empirical demographic data, we measure the reachability of this disease model and perform disease simulations over a range of latent period durations. Results: We find that maximum transmission risk results when the disease latent period (and thus the generation time) are synchronized with human circadian rhythms of 24 h, and minimum transmission risk when latent periods are out of phase with circadian rhythms by 12 h. The effect of this synchronization is present for a range of disease models with realistic disease parameters and host behavioral responses. Conclusions: The reproductive potential of pathogens is linked inextricably to the host social behavior required for transmission. We propose that future work should consider contact periodicity in models of disease dynamics, and suggest the possibility that disease control strategies may be designed to optimize against the effects of synchronization. Keywords: Reachability, Contact network, Transmission, Synchronization, Circadian rhythm, Latent period, Generation time

Background still remain about the complex interplay that emerges The prevention and mitigation of infectious disease out- from coupling the dynamics of human social behavior breaks remains a major challenge that crosses several with the life-cycle of a pathogen [9]. scientific disciplines. While advances in virology and After entering a human host, diseases typically expe- immunology remain crucial for the development of vac- rience a latent period. During this time, the pathogen cines and therapeutics, contributions from the social and multiplies within the host, but is yet unable to transmit behavioral sciences continue to improve our understand- to others. This is then followed by the infectious period, ing of disease transmission at the population scale [1, 2]. during which disease transmission is possible [10]. The Recent work in the field of network has latent period is closely related to the made important strides in our understanding of how the (the time between receiving the and the onset dynamics of individual and population social behavior of symptoms), but in many cases infectiousness precedes drive outbreaks [3–8]. However, many questions symptoms, resulting in a period of time for which the host is capable of transmission but unaware that they have been *Correspondence: [email protected] exposed to the infection [11, 12]. 1Department of Biology, Georgetown University, Washington, DC, 20057 USA

© The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Colman et al. BMC Infectious Diseases (2018) 18:219 Page 2 of 10

An additional aspect of disease dynamics is the behav- of opportunity for transmission to occur; this assumes a ioral responses of the host and the community follow- rapid reduction in social contact after the onset of infec- ing the onset of illness. Sickness behaviors such as fever, tiousness and therefore may not be appropriate for less lethargy, depression, and loss of appetite, cause the host virulent infectious diseases. to limit their movement and social interactions [13–16]. Biological rhythms are known to influence within-host These responses are thought to be adaptive as they protect infection dynamics, immune response, and transmission host resources, reduce pathogen reproduction, and pro- between hosts [24, 25]. There has been recent interest mote inclusive fitness by protecting the social group from in the idea that pathogens can adapt to take advantage infection [17]. In humans, transmission can be reduced of periodic changes to their environment. For example, significantly through social isolation or through the avoid- whose life-cycle synchronizes with the timing of ance behavior of other susceptible individuals [18, 19]. regular treatment may be more resistant to Here, we focus on the effect of social withdrawal behav- the drug than those who do not [26]. Our work is a iors on the spread of disease. While previous studies contribution to this growing area with a focus on the inter- have considered reduced or rewired contacts [20, 21], action between host social behavior cycles and pathogen we choose to examine the possibility that the infectious dynamics. period, which is typically estimated from survey data or controlled experiments [12, 22, 23], is effectively cut short Methods by the onset of sickness behaviors. Under these condi- The goal of our study is to use empirical contact data tions, it may be possible for diseases to have a reproduc- to reveal the presence and magnitude of the synchro- tive advantage when their latent period synchronizes with nization between contact dynamics and disease progres- the timing of human social behavior (see Fig. 1). sion. While the underlying concept may be relevant to To test this hypothesis, we use temporally resolved a range of infectious diseases, we focus specifically on human contact network data from various social settings a moderately-transmissible respiratory disease such as (a conference, a school, and a hospital) and ask how dis- influenza. After describing the empirical data used in this ease spread would fare in each of these networks. We also study we introduce a method to measure the contagion consider this question in semi-empirical networks which potential of a temporal contact network with respect to include both household and non-household contacts. We a disease with given latent and infectious period dura- primarily focus on diseases that have a short window tions. We then describe a method to quantify the effect

Fig. 1 Conceptual illustration showing the effect of different latent periods. In the upper panel, the host becomes infectious 12 h after receiving the infection, at which point he has entered a more sedentary phase of his daily schedule. The symptoms of the infection influence him to avoid returning to his school or workplace and no further transmission occurs. In the lower panel, the infectious period begins at the same time of the day that he received the infection. While the symptoms of the disease may result in social withdrawal, there is a period of time for which he is both infectious and socially active, giving the disease an opportunity to spread Colman et al. BMC Infectious Diseases (2018) 18:219 Page 3 of 10

of synchronization for simulated disease spread on a tem- were recorded over 4 days [29], and (c) a primary school in poral contact network, and lastly outline how we couple which 242 participants were recorded over 2 days [30, 31]. the disease simulation with three different host behavioral In a similar fashion to the original study [30], we looped responses. this data to produce a dataset spanning six weeks. We used the first day to represent Monday, Wednesday and Friday Data and the second day to represent Tuesday and Thursday. In the first two parts of our analysis we use human contact We then added 2 days of inactivity to replicate a typical data from the Sociopatterns project (sociopatterns.org), school week and weekend. and in the third part, we utilize synthetic networks based Because the data provided by each of the above stud- on demographic data from an urban area [27]. ies is limited to a single setting, we used another data Data relating to the kind of close-proximity interactions approach to consider the impact of more complete net- that allow respiratory diseases to transmit was down- works, including home contacts in addition to the non- loaded from the Sociopatterns website. The data has the home contacts captured in the datasets discussed above. format of a temporal network, meaning that for each inter- We used the procedure used in [27] (originally developed action recorded, we are given the identities of the two in [32]) to generate synthetic contact networks based on individuals involved, and the times for which the inter- empirical distributions of ages, household sizes, school action started and ended. We use human contact data and classroom sizes, hospital occupancy, workplaces, recorded in three separate locations and Sociopatterns and public spaces from the Greater Vancouver Regional studies. Participants wore radiofrequency identification District. (RFID) sensors that detect face-to-face proximity of other We generated a population with 1094 households, participants within 1 − 1.5 meters in 20-s intervals. Each which yielded 2692 individuals. Each member of this pop- data-set lists the identities of the people in contact, as ulation was assigned to activities according to their age, well as the 20-s interval of detection. To exclude contacts and edges between individuals were created based on their detected while participants momentarily walked past one location and nature of their overlapping daily activities. another, only contacts that are detected in at least two Full details of how edges were assigned can be found in consecutive intervals are considered interactions. [27]. For the present study we converted this static net- Sensors were not worn outside the locations being stud- work into a temporal network by adding times to the edges ied so there are long spans of inactivity corresponding to in the following way: we synthesize a typical weekday by the periods from early evening to early morning (See the assigning to all non-household contacts a start time at top panels of Fig. 2). The three data-sets used were: (a) a 8am and end time at 4pm and to household contacts a conference in which 110 participants were recorded over start time of 4pm and end time of 12am. A typical week- 3days[28], (b) a hospital ward in which 74 participants end day is created by assigning a start time of 8am and

Fig. 2 Reachability. The top panels show the number of face-to-face interactions between pairs of individuals (in the school data we only show 2 of the 6 weeks). The bottom panel shows the mean reachability of a disease over a range of latent periods. For the purpose of presentation we have subtracted the number of nodes reached directly from the seed (this is the same for all values of the latent period duration). The tendency for latent periods which are larger multiples of 24 h or 7 days to result in lower reachability is explained by the limited time span of the data-sets Colman et al. BMC Infectious Diseases (2018) 18:219 Page 4 of 10

end time of 12am to all household contacts. We then of the effective infectious period (between onset of infec- piece these days together to create six weeks of temporal tiousness and social withdrawal) [18], the proportion of network data. individuals that are asymptomatic [39, 40], and the perse- verance of individuals [13]. Here we describe how we use Measuring disease impact through reachability a computational disease model over the empirical contact The reachability of an individual, X,isdefinedasthenum- network data to measure the impact of synchronization ber of individuals that could potentially become infected and its sensitivity to changes in each of these variables. given that X is the source of infection [33–36]. The orig- The disease simulation, based on an SEIR model (fully inal definition applied only to contagion processes where described in Section S1 and Figure S3 of the Additional each individual can be in one of only two states: suscepti- file 1), takes as input: the temporal contact data, a “seed” ble or infectious (i.e. an SI model). The concept has since individual from which the outbreak originates, the time been developed to incorporate the recovered state (i.e. an for which the seed becomes infectious, and the following SIR model) [37]. Here, we have further extended the con- disease parameters: β, the per-second probability of trans- cept of reachability to include a latent state of infection mission during contact between an infectious individual (i.e. an SEIR model). and a susceptible one; the mode of the latent period dis- We compute the reachability of X withrespecttoagiven ˆ tribution, E; the dispersion of the distribution of latent ( ) set of disease parameters; namely, the latent period, E, E periods σg ; the mode of the effective infectious period which is the length of time from when an individual is distribution, ˆ ;perseveranceofthepopulation,1/k , exposed to infection to the time they are able to trans- I I which we define as the reciprocal of the shape parameter mit to others (more commonly called the “Exposed” state); of the effective infectious period distribution and which and the effective infectious period,  , which is defined I captures the variation in host response to disease; and the as the length of time a host remains infectious after the proportion of exposed individuals that are asymptomatic, latent period has elapsed. To capture the impact of sick- a, who do not experience symptoms or sickness behaviors, ness behaviors, we will assume very short durations for and thus experience a longer effective infectious period  . The host may experience illness for longer (the true I of  =  . By using the modes of the distributions infectious period, which we denote  ) but, due to the lack I J J of  and  , and not the mean, we are able to vary of social interactions, there are no transmission events E I the frequency of large outliers through dispersion and possible after  . I perseverancewhilekeepingtheoutcomeforthetypical We say that a member of the population, X,can“reach” individual at a specific value. another, Z, if a sequence of contacts exists that makes it feasible for a pathogen to spread from X to Z. For this to be According to our hypothesis, we expect the number of the case, the time between any two consecutive contacts in disease cases to be largest when the generation times of the outbreak are close to multiples of 24 h. The gener- thesequencemustbegreaterthanE and less than E + ation time for a transmission event is the time between I (see Figure S1 in the Additional file 1). We impose one further restriction that the sequence must begin during the moment the host received the infection and the moment they transmitted it to another individual. Since the period of length I that starts when X is first observed interacting. This represents a situation in which X arrives the expected time between the onset of infectiousness and ˆ / inthesysteminaninfectiousstate. transmission is I 2 h (assuming times are dis- We have chosen to use reachability as it incorporates tributed uniformly over the effective infectious period), ˆ + ˆ / the relevant elements of disease dynamics while also being the expected generation time is E I 2. We therefore relatively fast to compute. It does, however, make implicit expect to find the largest outbreaks to occur in the simu- ˆ = ˆ = assumptions about the dynamics of the disease in ques- lation when E 23 and the smallest when E 11; we tion. Specifically, it is assumed that the disease variables, use the difference between these two cases to measure the i.e. the latent and effective infectious period durations, effect of synchronization. are homogeneous across the population. To test whether More specifically, we select each individual, i,inthe the results obtained are sensitive to these assumptions, population as the seed of the outbreak, and the time of we perform disease simulations on the same data using a their first contact as the start of their effective infec- computation model. tious period. The outbreak is allowed to proceed as per the SEIR model and is complete when there are Measuring the effect of synchronization no longer any infected individuals in the population, Real diseases exhibit a range of dynamical behaviors that or when there are no more contacts in the popula- may invalidate the results obtained through the analytical tion (due to the limitation of the datasets). This is ˆ approach of reachability. For example, there may be vari- repeated 100 times for each individual, i,withE = ˆ ationinthedistributionoflatentperiods[38], the length 11 h and another 100 times with E = 23 h. To Colman et al. BMC Infectious Diseases (2018) 18:219 Page 5 of 10

measure the magnitude of the outbreak, we calculate the For the conference setting we observe peaks in mean number of infected individuals across these sim- reachability when the latent period is 24 or 48 h. The peak ˆ ˆ (E) ulations and denote this as I i, β, E, I , J , σg , kI , a . corresponding to a latent period of 24 h is larger than the We note that we do not include the seed, or those size of the peak corresponding to an approximate 48-h infected directly by the seed, in this calculation so latent period. In the first case, those infected by the seed as to exclude infections that have no relation to the on day one, can cause a second generation of infections on latent period. The synchronization effect for an individ- day two, which then causes a third generation infections ˆ ˆ (E) on day three. In the second case only two generations of ual i is defined as I i, β, E = 23, I, J , σg , kI, a −   infection are possible. β ˆ = ˆ  σ (E) I i, , E 11, I, J , g , kI, a . Similarly, in the hospital setting we observe four peaks in reachability. The largest peak corresponds to a 24-h Measuring disease impact with household contacts latent period and represents generations of infection that Given the different structure of the urban contact net- reproduced on days 2-5 of the hospital contact dataset. work model, we specify further the disease simulation The peak corresponding with a 48-h generation time rep- algorithm on this network. Here, the disease simulation resents a disease that was able to reproduce on only begins with a seed becoming infectious at a random time 2ofthe5days(2and4daysafterthetimetheseed during the first 24 h of the synthetic temporal contact was infectious). The final two peaks represent the opti- network (which happens to be a Monday). To quantify mal latent periods in cases where only 1 generation of the impact of household contacts on the synchronization infections is possible due to the limited time frame of effect, we consider three models: (I) No sickness behavior the data. is implemented. Individuals are infectious for the entirety Results for the school setting show a comparable pat-   of the true infectious period, i.e. I = J . We assume that tern but on a larger time-scale. In this data, all individuals β the transmission probability, , is lower in this case to are seeded on day 1; the peak in reachability correspond- make the results comparable to the remaining cases (see ing with a 24-h generation time includes infections that Additional file 1: Section S2.1). (II) Sickness behavior leads occurred on days 2-5; since no contacts occur on week- to social withdrawal from non-home contacts only. This ends, the disease dies out on Day 6 (Saturday). Peaks withdrawal takes effect the day after infectiousness begins corresponding to generation times of 2 days and 4 corre- (details are described in Additional file 1:SectionS2.1). spond to outbreaks that can only survive for 2 generations Lastly, (III) extreme sickness behavior is implemented (as of infection. In both of these scenarios, the disease also    we did with the RFID data) and I J .Thus,infected dies out over the weekend. The absolute maximum reach- individuals socially withdraw from all contacts (home and ability corresponds to a latent period of 7 days. This peak non-home). occurs because infections caused by the seed on the first day are able to reproduce on the same day of the follow- Results ing week, a third generation can again occur on the same InthethreeRFIDcontactnetworks,therateofcontact day of the next week, and this pattern can continue for all between individuals fluctuates periodically in time with six weeks of the data. with latent period dura- the cycles of human social activity (see Fig. 2). By con- tions that are not a multiple of 7 days will eventually die sidering the spread of disease through these networks, we out because of the absence of social contact during the find that the impact of infectious disease is maximized weekends. when timing of infectiousness is synchronized with these temporal dynamics. We show this through analytical mea- surement of the temporal network structure (reachability) Robustness of the synchronization effect and test the robustness of these results through analysis of To consider the sensitivity of the synchronization effect to simulated disease outbreaks on each network. We further realistic variability in pathogen or host behavior charac- show that similar synchronization occurs for outbreaks on teristics, we simulated disease outbreaks on the empirical a larger scale, and with various types of contact, using the contact data over a range of parameter values. For the urban contact network data. initial baseline parameters, we assume a latent period dis- (E) persion factor of σg = 1.1 which represents the low, Influence of the latent period on disease impact yet realistic, value for respiratory infections [41]. We set To reveal the epidemiological impact of the timing of the mode of the effective infectious duration distribu- ˆ infectiousness, we computed the mean reachability (over tion, I = 2 h. (While we are unaware of empirical data all individuals in the network) for a range of latent periods measurements of I ,[42] report an average of 8.5 work and an effective infectious period of I = 2. The results hours are lost due to severe common colds). We set a true are shown in Fig. 2. infectious period of J = 24 h, following [43]. We also Colman et al. BMC Infectious Diseases (2018) 18:219 Page 6 of 10

assume that the asymptomatic proportion, a = 0and Increasing perseverance (i.e. the variation in the time perseverance, 1/kI = 0.2. to social withdrawal among infectious individuals) leads In this baseline case, the synchronization effect was to longer periods of infectiousness for some individuals, positive, i.e. changing the mode value of the latent dura- and consequently allows for more opportunities for trans- ˆ ˆ tion distribution from E = 11 to E = 23 yielded mission. In Fig. 3, we see that the relationship between an increase in the number of infections. This is consis- perseverance and synchronization effect is qualitatively tent with the results of the previous section (Influence similar to that seen for the asymptotic proportion; at low of the latent period on disease impact). We then tested values, perseverance benefits both the non-synchronized the robustness of this effect by perturbing each parameter andsynchronizeddiseases.Forlargervalues,theindi- away from its baseline value towards more realistic sce- viduals who persevere for prolonged durations dominate narios (Fig. 3). The following paragraphs report the effect transmission and the time at which they first become of each parameter perturbation. infectious loses significance. Since asymptomatic individuals remain in the system for ( ) Dispersion in the distribution of latent periods, σ E , significantly longer than those who do experience symp- g affects the mean outbreak size differently depending on toms, their presence increases the overall outbreak size. the value of ˆ .Forˆ = 11, as dispersion increases, the Moreover, since the time at which they first become infec- E E probability that the latent period will be close to 11 gets tious has relatively little affect on the number of infections smaller and the probability that the effective infectious they cause, we expect to see a decrease in the synchroniza- period will intersect with a period of high social activity tion effect as a increases. This was found to be the case for gets larger. The opposite is true for ˆ = 23. Increas- moderate proportions of asymptomatic individuals (0.1 < E σ (E) a < 0.3); however, at lower values, the presence of asymp- ing g therefore causes the difference in mean outbreak tomatic individuals did not benefit the non-synchronized sizes of the two cases to converge towards zero. ˆ disease significantly more than the synchronized one. As the effective infectious period, I, increases, there This is seen most clearly in the school setting, in which are two consequences: outbreaks become larger as there the synchronization effect was actually amplified by the is more time for transmission, and the exact duration ˆ addition of asymptomatic cases. The asymptomatic pro- of the latent period, E, becomes less significant since portion for influenza has been estimated to be within infected hosts spend a larger fraction of a 24-h period in 4 − 28% [44], making the relevance of synchronization for an infectious state (and are thus more likely to have social influenza unclear. interactions while infectious, regardless of when their

Fig. 3 The effect of synchronization. The dark line represents the median effect size over individuals in the population. The effect size is defined as the increase in mean outbreak size between a disease for which the latent periods follow a log-Normal distribution with a mode of 11 h, and one which has a mode of 23 h (dispersion factors are equal). Points correspond to the values on the horizontal axis for which the effect size was computed and the gray area is the inter-quartile range. We see that the synchronization effect observed in “Influence of the latent period on disease impact” Section is present for a wide range of parameters values in the disease model Colman et al. BMC Infectious Diseases (2018) 18:219 Page 7 of 10

infectiousness began). Consequently, we find that the syn- spread between schools and workplaces [45], contribut- ˆ chronization effect is maximized at approximately I = 6 ing more to the size of the outbreak than does the effect h; here, the effective infectious period is long enough for of synchronization. We present the results of our epi- a relatively large number of infections to occur, but short demic simulations on the urban contact network model to enough that it can be entirely absorbed by periods of low address this question. activity in the asynchronous case. In the first model (I), we consider epidemic outcomes In the conference and hospital settings, the number of when infected individuals do not change their behavior generations of infection is limited by the duration of the in any way and I = J = 24 h. In Fig. 4,weseethat data (3 and 4 days, respectively). In general, this gives the duration of the latent period has little effect on the the shorter latent period an advantage over the longer disease outcomes. However, even in the absence of sick- one, and we eventually see the synchronization effect go ness behavior, epidemics are more likely to occur at values below zero. In the primary school dataset, on the other around 18 h. hand, most infections die out before the end of the 6-week In the second model (II) illness does not affect house- duration and the synchronization effect is rarely negative. hold contacts. We assume that if an individual becomes symptomatic during home hours, they will stay at home; Effect of household contacts and if the individual becomes symptomatic during the Since the hospital, school, and conference datasets do not daytime, they will continue to engage in non-household include interactions that occur outside of their established social contacts until the end of the day. Epidemics occur settings, it is necessary to ask whether the synchroniza- when the latent period is close to 20 and 42 h. We note tion effect would be found in a complete contact net- that large epidemics are likely across a larger range of work which included long-duration home contacts during latent period modes in the second cluster due to the larger evenings and weekends. The effect of these missing links variance in the distribution of latent periods. This is a could be significant enough to break the synchronization consequence of the fact that incubation (and thus latent) pattern we see. For example, interactions that occur in periods follow a log-Normal distribution for which higher the household may act as bridges that allow infection to mean results in a higher variance [46].

Fig. 4 Simulated outbreaks in a synthetic urban environment The proportion of outbreaks that exceed a given size are shown (for each latent period 103 simulations were performed starting from randomly selected seeds at random times during the first day). The three models shown are described in “Effect of household contacts”Section Colman et al. BMC Infectious Diseases (2018) 18:219 Page 8 of 10

The third model (III) is similar to that used in the reach- synchronization with human circadian cycles should be ability analysis, where infected individuals withdraw from advantageous for an infectious disease, this is only true all contacts after 2 h of infectiousness. This results in a when the window of opportunity for transmission is suit- similar synchronization pattern as model II, however, as ably short. In some cases symptoms coincide with infec- we might expect from a typically shorter infectious period, tiousness closely enough to induce a rapid behavioral the latent period durations that correspond to epidemics response from the host and be consistent with our results are more tightly clustered (around 23 and 46 h). [11, 12, 48], while others exhibit much longer periods of pre-symptomatic viral shedding that would be unaffected Discussion by human circadian rhythms [23]. However, even in these The reproductive potential of a pathogen is driven by cases there is doubt that transmission occurs before the the host social behavior that underlies transmission. We onset of symptoms [49]. Another possibility that would have considered the class of diseases that causes hosts invalidate our model is if infectiousness persists after the to socially withdraw due to symptoms, and focused on end of symptoms but evidence suggests that this does not the role that the latent period plays in determining their occur for influenza [11]. epidemic potential. Our results support the hypothesis Behaviorally, we make a number of simplifying assump- that disease risk can be amplified by synchronization tions about social distancing and contact patterns. For between the latent period of the infection and the circa- one, we assume that behavior change by infected individ- dian rhythms of the host population. uals eliminates transmission potential entirely, but there Through analysis of empirical face-to-face contact net- may be more variation in this change. Second, we ignore works, we have shown that a disease is most pervasive that social isolation could also result from susceptible when its generation time is close to a multiple of 24 h. individuals avoiding symptomatic infected individuals; In such cases, infections that occur during a socially busy these responses may be driven by public awareness of the time of day will likely cause another generation of infec- epidemic and therefore change dynamically as it grows in tions during the same socially active time on a subsequent size [50]. Third, the contact network data we use in this day, thus perpetuating the life-cycle of the pathogen. Con- study do not represent the range of human social behav- versely, we observe minimum disease risk when the gener- ior heterogeneity: the RFID contact networks neglect any ation time is out-of-phase with human circadian rhythms influence from outside the selected location, and the by exactly half a day. In this case, individuals infected dur- urban contact network model assumes temporal homo- ing socially busy times will become infectious during a geneity in contact dynamics. In combination, however, time when there are fewer opportunities for transmission. our results do provide qualitative insights into the impact The results of our final analysis illustrate that the avoid- of partial social withdrawal. ance or non-avoidance of contact with household mem- The results of this analysis suggest that by having a life- bers in the evening has limited effect on the optimal cycle that synchronizes with the circadian cycles of human generation time of the disease. In all models of that anal- behavior a pathogen can gain a reproductive advantage ysis, a significant fraction of transmission occurs through over those that do not. If this hypothesis holds, we would household contact (53%, 67% and 44% for models I, II and expect to see the generation times of diseases to be close III, respectively) suggesting that the the period of social to multiples of 24 h. A recent review of serial intervals inactivity during sleeping hours is the main opponent to (which are closely related to generation times if symptoms the disease (and the reason why epidemics die out faster and infectiousness track each other) reported the mean when the latent period is not synchronized). This is most and standard deviation from seven influenza studies [51]. apparent in Models II and III, which could be said to be In all reported cases, the mean generation time was within more virulent than Model I (higher transmission prob- 0.3 days of perfect synchronization; the probability that abilities and more likely to provoke social withdrawal). this would occur by chance is less than 0.1. Moreover, five In the trade-off between transmissibility and life history of these cases were out of phase by 0.2 days or less, and the traits, this result suggests a novel advantage to being less two that were further from synchronization had variances virulent [47]. that were above the average. These data are consistent Our modeling approach has a number of limita- with the idea that for influenza to reach epidemic scale, tions. Biologically, we have assumed that the popula- its generation time must either synchronize with human tion is homogeneously and perfectly susceptible. While circadian rhythms, or have highly variable latent period this assumption would be invalidated with pre-existing durations. natural or vaccine-induced immunity in the host popu- The conclusions of this work have implications for pre- lation, we expect our results to hold given any periodic- dicting and controlling infectious disease transmission at ity in the contact patterns of the remaining susceptible the population scale. Contact rates vary dynamically, both population. Additionally, while our results indicate that periodically according to cycles of human behavior, and Colman et al. BMC Infectious Diseases (2018) 18:219 Page 9 of 10

in response to the disease itself. Consequently, the win- the consequences of disease synchronization, and, more dow of opportunity for transmission may be much shorter broadly, the complex interactions that can occur between than the actual duration of infectiousness determined in social and biological systems. experimental studies; thus, the important question is not How long is the infectious period?,butratherWhen does Additional file the infectious period begin?. Epidemic models that do not consider the effect of sickness behaviors, and assume a constant (non-cyclic) Additional file 1: Supplementary information. (PDF 904 kb) rate of contact, may lead to misleading conclusions about Acknowledgements the drivers of transmission. This is most likely to apply We would like to thank Chad Wells, Jon Zelner, Adam Kucharski, and Dan to cases where sickness behaviors are strong and infec- Yamin for their invaluable feedback. tiousness begins shortly before the onset of symptoms. Previous work has drawn attention to the importance of Funding This work was supported by NSF Grant No. 1414296 as part of the joint this period, suggesting that control strategies involving NSF-NIH-USDA Ecology and Evolution of Infectious Diseases program. the treatment or isolation of symptomatic individuals are only effective if individuals can acknowledge that they Availability of data and materials have the disease within a reasonable amount of time [18]. The datasets generated and/or analyzed during the current study are available as part of the Sociopatterns Project, http://Sociopatterns.org.Alldatausedin Our work suggests that, in such cases, the duration of the this study, including the semi-synthetic urban population network, and the latent period becomes a primary driver of transmission simulation code are available at https://github.com/EwanColman/Disease- patterns. simulation-on-temporal-network-data.

Finally, we suggest the possibility that control strate- Authors’ contributions gies for managing infectious disease may be designed KS conducted the analysis of reachability and EC created and analyzed the around the effects of synchronization. For example, antivi- disease simulations. EC and SB conceived and designed the analysis and interpreted the results. EC and KS contributed to the writing of the rals for influenza are expected to alleviate symptoms if manuscript. EC and SB edited the manuscript. All authors have read and taken within 24 h of symptom onset. Our results sug- approved the manuscript. gest that if antivirals eliminate transmissibility (which Ethics approval and consent to participate does not appear to be supported for influenza, [52]), it Not applicable. would be possible to optimally time antiviral adminis- tration to minimize cases by making the period from Competing interests exposure to antiviral onset out of phase with human cir- The authors declare that they have no competing interests. cadian rhythms. As another example, the manipulation of Publisher’s Note school and workplace schedules to break the synchroniza- Springer Nature remains neutral with regard to jurisdictional claims in tion effect may result in a hostile environment towards published maps and institutional affiliations. infections with particular latent periods. More generally, Received: 23 August 2017 Accepted: 25 April 2018 a better understanding of the coupling between human and disease dynamics could lead to methods of social dis- tancing that are sensitive to the temporal dynamics of References 1. Manfredi P, D’Onofrio A. Modeling the Interplay Between Human infectious disease. Behavior and the Spread of Infectious Diseases. 1st edn. Verlag: Springer; 2013. Conclusions 2. Heesterbeek H, Anderson RM, Andreasen V, Bansal S, De Angelis D, Dye C, Eames KT, Edmunds WJ, Frost SD, Funk S, et al. Modeling We have proposed the hypothesis that infectious diseases infectious disease dynamics in the complex landscape of global health. are most pervasive when their latent period, and con- Science. 2015;347(6227):4339. sequently their generation times, are synchronized with 3. Bansal S, Grenfell B, Meyers LA. When individual behaviour matters: homogeneous and network models in epidemiology. J R Soc Interface. circadian rhythms of the host population. We predict 2007;4(16):879–91. that synchronization is most likely to occur for diseases 4. Masuda N, Holme P. Predicting and controlling infectious disease that invoke a strong symptomatic response and lead to epidemics using temporal networks. F1000prime reports. 2013;5:. 5. Holme P. Temporal network structures controlling disease spreading. a withdrawal of social contact in the host. Our analy- Physical Review E. 2016;94(2):022305. sis of empirical temporal contact networks supports this 6. Pastor-Satorras R, Castellano C, Van Mieghem P, Vespignani A. Epidemic argument by showing that the reachability of a disease is processes in complex networks. Rev Mod Phys. 2015;87:925–79. 7. Sah P, Mann J, Bansal S. Disease implications of animal social network strongly dependent on its latent period and that simulated structure: a synthesis across social systems. J Anim Ecol. 2017;87(3): diseases that synchronize with the daily rhythms of social 546–58. contact gain a reproductive advantage over those that do 8. Colman E, Bansal S. Social fluidity mobilizes infectious disease in human and animal populations. bioRxiv, 170266. 2017. not. We conclude that the surveillance, modeling, and 9. Funk S, Bansal S, Bauch CT, Eames KTD, Edmunds WJ, Galvani AP, mitigation of infectious diseases should carefully consider Klepac P. Nine challenges in incorporating the dynamics of behaviour in Colman et al. BMC Infectious Diseases (2018) 18:219 Page 10 of 10

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