Many behavioral phenomena have been found to spread interpersonally through social networks, in a manner similar to infectious diseases. An important difference between social contagion and traditional infectious diseases, however, is that behavioral phenomena can be acquired by non-social mechanisms as well as through social transmission. We introduce a novel theoretical framework for studying these phenomena (the SISa model) by adapting a classic disease model to include the possibility for ‘automatic’ (or ‘spontaneous’) non-social infection. We provide an example of the use of this framework by examining the spread of obesity in the Framingham Heart Study Network. The interaction assumptions of the model are validated using longitudinal network transmission data. We find that the current rate of becoming obese is 2 per year and increases by 0.5 percentage points for each obese social contact. The rate of recovering from obesity is 4 per year, and does not depend on the number of non-obese contacts. The model predicts a long-term obesity prevalence of approximately 42 , and can be used to evaluate the effect of different interventions on steady-state obesity. Model predictions quantitatively reproduce the actual historical time course for the prevalence of obesity. We find that since the 1970s, the rate of recovery from obesity has remained relatively constant, while the rates of both spontaneous infection and transmission have steadily increased over time. This suggests that the obesity epidemic may be driven by increasing rates of becoming obese, both spontaneously and transmissively, rather than by decreasing rates of losing weight. A key feature of the SISa model is its ability to characterize the relative importance of social transmission by quantitatively comparing rates of spontaneous versus contagious infection. It provides a theoretical framework for studying the interpersonal spread of any state that may also arise spontaneously, such as emotions, behaviors, health states, ideas or diseases with reservoirs.

Information, trends, behaviors and even health states may spread between contacts in a social network, similar to disease transmission. However, a major difference is that as well as being spread infectiously, it is possible to acquire this state spontaneously. For example, you can gain knowledge of a particular piece of information either by being told about it, or by discovering it yourself. In this paper we introduce a mathematical modeling framework that allows us to compare the dynamics of these social contagions to traditional infectious diseases. We can also extract and compare the rates of spontaneous versus contagious acquisition of a behavior from longitudinal data and can use this to predict the implications for future prevalence and control strategies. As an example, we study the spread of obesity, and find that the current rate of becoming obese is about 2 per year and increases by 0.5 percentage points for each obese social contact, while the rate of recovering from obesity is 4 per year. The rates of spontaneous infection and transmission have steadily increased over time since 1970, driving the increase in obesity prevalence. Our model thus provides a quantitative way to analyze the strength and implications of social contagions.

Funding: This work was supported by the National Institute on Aging grant P01 AG031093, the John Templeton Foundation, the Bill and Melinda Gates Foundation, the National Science Foundation/National Institutes of Health joint program in mathematical biology (National Institutes of Health Grant R01GM078986), and graduate fellowships from the National Science Foundation and the Canadian Natural Sciences and Engineering Research Council. NHLBI's Framingham Heart Study is supported by contract number N01-HC-25195. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Here, we introduce a new model to study the spread of entities in a social network which has all of the important properties listed above. We then analyze its characteristics and show how it can be applied in different contexts. This model is an extension of the classical infectious disease model, combining features from other models mentioned above. It describes infections that can be contracted both spontaneously and through social (network-structured) transmission, and allows for recovery from infection. As an example, we focus on the spread of obesity in the Framingham Heart Study (FHS) network. The interaction assumptions of the model will be validated using longitudinal network transmission data. We show how we can quantitatively assess the values for the rate of adopting a trend spontaneously versus by contagion to determine the extent to which social transmission is important. We use it to predict prevalences and intervention effectiveness (i.e. get quantitative output, not just qualitative behavior). The results of this model are very different from models with other interaction assumptions, such as the ‘majority rules’ models. We will show that transmissive components are often small compared to the automatic component, but may still contribute materially to prevalence levels. Lastly, we will use pair-wise approximations to generate analytic results for infections in network-structured populations, as well as presenting simulations using a real social network.

Each of these models, however, has one or more properties that are problematic for studying social contagion. Many do not capture the probabilistic nature of contagion, or the asymmetry inherent in traditional infectious disease (where the infected state spreads through social contagion whereas the non-infected state does not). Others only consider well-mixed populations, where everyone is influenced by everyone else, ignoring the effect of network structure. Most models inspired by epidemiology are not directly applicable to the social spread of other phenomenon, because many phenomena that spread by social contagion may also arise spontaneously. That is, it is possible to adopt a trend or behavior, or obtain information, from an outside source, without directly ‘catching’ it from a contact in the network. In other words, on top of the probability of obtaining the infection from each infected contact, there is also a non-zero probability of ‘automatically’ obtaining the infection, independent of the local network. This ‘automatic’ non-social infection is not included in traditional infectious disease models. Economic models for the diffusion of innovations, based on early work by Bass [34] , do take into account ‘automatic’ infection. Individuals move from ‘susceptible’ (non-adopter) to an infected (adopter) state by adopting a new product or idea, influenced by both social and non-social factors. However, these models do not allow for recovery; because the innovation adoptions are assumed to be permanent changes in behavior, individuals never move back to a susceptible state. This results in the entire population becoming adopters at equilibrium. This does not reflect the dynamics of many phenomena that spread socially, which may be repeatedly acquired and lost (for example, happiness or obesity). Through a balance of infection and recovery, a steady-state with multiple states of individuals coexisting can be reached. Finally, most previous models make assumptions about the type of interaction between individuals, the particulars of which are not usually validated with real data. Yet, long term behavior of a model and the prevention strategies it suggests can depend critically on the specifics of the interaction assumptions.

Within network studies, much work has focused on how information, trends, behaviors and other entities spread between the individuals in social networks. These processes are generally referred to as ‘contagion’. Such suggestions of contagious dynamics and the possible relevance of network structure can be rigorously examined using mathematical models of contagious processes. These can then be used to obtain accurate measures of expected prevalences, interventional efficacy, and optimized information flow. Many previous models have been proposed to study influential interactions between individuals. Most of these have considered well-mixed populations, although more recent work has focused on network-structured populations. The most well studied are classic epidemiological models (like SIS and SIR) for the spread of microbial infectious diseases [26] , including spread in network-structured populations [27] – [30] , [31] , [15] . Various related processes have been used to model social influence, with important contributions including the same epidemiological models [32] , [33] , diffusion models [8] , [34] – [38] , statistical mechanics type interactions [39] , [40] , and threshold models [41] (reviewed by Jackson [1] and Newman et al. [42] ).

Social network effects are of great importance for understanding human behavior. People interact with a varying number of individuals and with some individuals more than others, and this affects behavior in fundamental ways. Sociologists have long studied social influence through networks, and networks now routinely appear in investigations from other fields, including economics [1] , physics [2] , public health [3] and scientific publishing [4] , [5] . Extensive reviews of social networks analysis, including investigations of their structure and their effect on social dynamics, include Mitchell [6] , Wasserman [7] ,Watts [2] , Rogers [8] , Jackson [1] , and Smith [9] . Networks have also long been known to be important in many areas of biology (reviewed by [10] ), including ecological food webs and the evolution of cooperation [11] – [14] . Social networks have also been studied as determinants of health (reviewed by Smith [9] ), ranging from determining the patterns of infectious disease spread [15] to the propagation of phenomena such as emotions [16] – [18] , smoking cessation [19] , obesity [20] , suicide [21] , altruism [22] , anti-social behavior [23] , and online health forum participation [24] . These studies suggest that on top of the physical environment, the social environment can also be an important contributor to health. They have lead to suggestions that public health interventions must be designed that work with the network structure and that the network can be exploited to spread health related information [9] , [25] .

Analyzing the n-regular pair-wise equations allows us to get analytic results and determine how and under what conditions network structure affects the spread of behaviors which are both spontaneously acquired and spread interpersonally. Although simple closed-form solutions do not exist when is non-zero, these equations can easily be integrated or numerically solved to get solutions. These equations ignore heterogeneities in the number of edges for different individuals, which can facilitate spread under some conditions (see supplement Text S1 for extension). Full stochastic simulations on large networks can be carried out to determine how and when the results differ.

The result of a network structure is that the number of partnerships between susceptible and infected individuals quickly becomes less than if random, and so . We can compare Eq. 7 to the well mixed result (Eq. 2), and see that the effect of the network is to lower the effective transmission rate by a factor of , and hence lower the prevalence, due to these correlations that build up locally. The larger is compared to , the more network effects are important. If infection is mostly automatic (when 0), the network no longer matters. Equation 7 actually holds generally (for any homogeneous network and any value), while Equations 8 and 9 are only applicable with = 0.

Here [XYZ] represents the number of situations where and X individual is connected to a Y individual who in turn is connected to a Z individual. We can approximate all these triples in terms of pairs, using a moment closure approximation ( [43] , Text S1 ), which then reduces the number of variables to three also. Then these equations can be simplified to (5)with (6)where is the number of contacts each individual has and is the transitivity of the network (the ratio of triangles to triples). Having a simplified set of equations is very useful for understanding contagion dynamics in structured populations. Integrating equations is much faster than running simulations on large networks, and from them analytic results can be derived which allows determination of parameter dependence. These equations assume that the local neighborhood for each individual is identical, that is, everyone has the same number of contacts ( ) and the same . They thus take into account the effects of fixed network structure but not heterogeneities between individuals. In the Supplementary Information ( Text S1 ) we have included the extension of these equations to include heterogeneities. These equations can be used to easily simulate disease spread and get expected steady state prevalences and correlations, which are very useful approximations and give insight into parameter dependence. Later, we will compare these equations to results from full simulations on realistic networks. When (which is approximately the case for most random graphs) we can get a closed-form solution for the prevalence at steady state: (7) (8) (9)

There are no analytic methods to solve SIS-type dynamics on arbitrary networks without making approximations. Thus, simulations are a more accurate tool to explore theoretical disease dynamics in structured populations without making simplifying assumptions about the network structure. For scaled, well-mixed populations, the formulas given in the previous sections for and are good approximations if is replaced with , the average contacts at a given time, while fixed networks, especially if non-uniform and highly inter-connected, can deviate from these values significantly. We can use a pair-wise approximation [29] , [43] , [44] to formulate the infectious process on a network structure in terms of differential equations. The fundamental variables are numbers of individuals of each type, and also the pairs of individuals, [XY] (where the edges are not directional). Because [XY] = [YX], and the total individuals and total edges is constant, the system can be reduced to three equations. (4)

The correlation between infected individuals, , rises above one as the epidemic proceeds, due to cluster formation as infected individuals transmit to their contacts. Similarly, the correlation between infected and susceptible individuals, , drops below one. The deviation of these correlations from 1 increases with (i) the ratio of transmissive infection ( ) to spontaneous infection ( ) in our model (there are no correlations without a transmissive component), and (ii) the inter-connectivity (transitivity) of the network. As a result of these spatial correlations, diseases on networks can progress more slowly than their well-mixed counterparts, leading to lower basic reproductive ratios. However, heterogeneity in the number of contacts per individual acts to increase . For two networks with the same average degree, if one has a larger variance in degree, then will be increased. Thus, it is possible for diseases on networks to have lower (or nonexistent) thresholds for endemic epidemics.

Traditional models of infection assume that the population is well-mixed. However, this assumption is unrealistic for many diseases, and also for the social spread of trends and behaviors. To account for the population structure, the infectious process can be constrained to take place on a social network. An infected individual can only pass their infection on to the suspectibles to whom they are connected. Properties of the infectious process thus depend on both the epidemiological parameters and the network structure, and there are often no longer simple analytic formulas to describe the reproductive ratio or steady state level of infection. For example, a property of disease spread on networks are spatial correlations (in the network sense) that arise between individuals in the same state. This correlation is defined as the ratio of the observed number of connections between two types of individuals to the number of connections expected if the positioning of individuals in the network was random. Spatial correlations of like individuals can be caused by an infective process spreading within a network [29] , but may also be caused by confounding environmental factors which similarly influence the behavior of connected individuals, or the formation of contacts based on similar behavior (also called homophily). For a network of N individuals with a total of E connections between them, the correlation between two states X and Y is defined by: (3)

In the infectious disease literature, a disease is said to be ‘endemic’ if a stable, non-zero fraction of the population is infected at steady state. If a single infected individual is introduced to a totally susceptible population, then the average number of secondary infections they cause before recovery is called the basic reproductive ratio, . For the regular SIS model in a well-mixed population of N individuals, . An epidemic, leading to an endemic equilibrium, only occurs for , and hence is a fundamental quantity used to describe and compare infectious diseases. For the SISa model, an epidemic occurs for all parameter values, due to the spontaneous infection term. Thus, social behaviors that can be adopted independently of neighbors mean that there is no longer a threshold for the behavior to become prevalent in a population, and even in the absence of contagion there would be a non-zero steady state prevalence. Because of this, there is not an obvious definition for in the SISa model. The steady state fraction of infected individuals in a well-mixed population is given by Eq. 2. (2)

There are three processes by which an individual's state can change. (i) An infected individual transmits infection to a susceptible contact with rate . (ii) A susceptible individual spontaneously becomes infected at rate , regardless of the state of their contacts. (iii) An infected individual returns to being susceptible at rate , independent of the state of their contacts.

In the standard SIS model, infection can only be transmitted by having a contact between an infected and a susceptible individual. Social ‘infections’, however, can also arise due to spontaneous factors other than transmission. Therefore, we extend the SIS model by adding a term whereby uninfected individuals spontaneously (or ‘automatically’) become infected at a constant rate , independent of infected contacts. A diagrammatic representation of our modified SIS model, which we will call SISa, is shown in Figure 1 . The corresponding differential equations for a well-mixed population are described in Eq. 1 (1)where is the number of infected individuals, is the number of susceptible individuals, is the population size, is the transmission rate, is the recovery rate, and is the rate of spontaneous infection. This model assumes a constant population size and neglects birth and death. The SISa model is related to infectious disease models with ‘imports’ (migration of infecteds into the population), although here the rate of spontaneous infection is proportional to the number of susceptibles, while in import models it is a constant or proportional to the total population size.

In the simplest infectious disease models [26] , individuals are classified as occupying one of two states: ‘susceptible’, meaning they do not have the disease, and ‘infected’, meaning they do have the disease. The disease can be transmitted to a susceptible person when they come into contact with an infected person. The rate of this disease transmission from infected to susceptible is defined as , the transmission rate. Once an individual is infected, they recover from the disease at a constant rate , regardless of their contacts with susceptibles or infecteds. In one class of disease models (susceptible-infected-recovered, or SIR), recovered individuals become immune to further infection and enter a ‘recovered’ state. However, behaviors, trends, health states, etc, can occur many times over an individual's life, and therefore we assume infected individuals return to the susceptible state after recovering. This form of susceptible-infected-susceptible (SIS) model is used to model infectious diseases that do not confer immunity, like many STDs.

Results

Calibrating model with FHS Network data The SISa model provides a formal way for assessing the social contagion of trends and behaviors that may be repeatedly caught and recovered from. Using data from the Framingham Heart Study (FHS) [45] we tested the validity of this model and estimated transmission parameters for various health related behaviors, though the focus here is on obesity as an example. To both demonstrate that obesity can display infectious-disease-like dynamics, and to estimate values for the model parameter , and , we use dynamic information about transitions between states based on our multiple time points of data. For data points separated by time intervals ( ) smaller than the average time between transitions, the transition probabilities can be linearized. The probability of a transition from susceptible to infected after a time can be given by , and the probability of transition from infected to susceptible after time , by . It is necessary for the time between measurements to not be comparable to or greater than the average lifetime of a state to keep the probability of double transitions within a time interval low. This epidemiological approach to social contagion has important differences from other models which look at correlations in present and past states of connected individuals. Here, similar to others [16], [19], [20], [46] we look at how contacts influence the transitions between states, which better captures the nature of contagion. Since we use pre-existing social ties, we do not see effects from selection bias in choosing friends with similar states. Additionally, time invariant confounding events that lead to concurrent changes in connected individuals will not show up as contagion effects in this model. The dataset we use is a subset of individuals from the Framingham Heart Study [45]. This study was initiated in 1948 in Framingham, Massachusetts and has continued enrolling subjects through the present. We examined individuals in the Offspring Cohort, enrolled starting in 1971. Subjects come to a central facility at regular intervals (approximately every 4 years) for medical examination and collection of other survey data. Body mass index (BMI) was measured at each exam, and obesity was defined as BMI 30 [47]. All other, lower, weights, which include underweight, normal range weight and over-weight, were classified as ‘not obese’. In additional to information on mental and physical health, subjects were asked to name at least one close friend at each exam, and were also connected to all first-order relatives, as well as coworkers and residential neighbors. For each subject, the following social connection data is available: (i) each other person to whom they were connected, (ii) the dates of initiation and termination of that relationship, (iii) the type of relationship (neighbour, coworker, first-degree relative, or friend), and (v) the geographic distance between the two subjects. The social network for each exam was constructed by creating a network matrix G, where if subject nominated subject as a connection before or during the time that subject was administered exam . All relationship types are mutual except for friendships, which are self-nominated, such that is possible for friendships. To study the transmission of obesity, we examine changes in BMI between sequential exams. Seven exams were administered to the Offspring Cohort between 1971 to 2001, with network data collected for each. We examine transitions occurring between each exam. The average fraction of the network that was classified as obese increased between these seven exams, suggesting the transmission process is not yet at steady state (Exam 1: 14 obese; Exam 7: 29 obese). Each set of exams were closely and consistently spaced ( (exam 1), (exam 7)). In general when modeling an infectious process, the rates of infection and recovery are assumed to be constant over time, with the prevalence changing as the infectious process begins and finally reaches equilibrium or is eliminated. When examining the spread of obesity using longitudinal data on transitions between exams, we can actually test this assumption and detect changes in the rates themselves. A given state is considered infectious if having more contacts in state makes you more likely to switch to state . That is, a positive relationship between the number of contacts in state and the probability to transition from state to state indicates that state is infectious with respect to state . Therefore, to test whether a given state is infectious with respect to another state , we perform an ordinary least squares (OLS) linear regression as follows. Each subject in state in exam N is coded as either having transitioned to state (transition = 1) or not (transition = 0) in exam N+1. We then regress this binary transition variable for each subject against the number of contacts in state that subject had during exam N. A significant positive correlation indicates that having more friends in state at the earlier exam makes you more likely to switch to state in the later exam. If state is infectious (a significant positive correlation exists), then the value of can be calculated from the slope of the regression line, and the value of can be calculated from the intercept. If state is not infectious (no significant correlation exists), then the value of can be calculated from the intercept. was taken as the average time between examinations, which varied between exams from 3 to 8 years. Using logistic regression as opposed to OLS regression gives very similar results, as the datapoint line is within the linear range of the logistic model. The structure of the Framingham Heart Study social network varies over the course of time, ranging from 7500 individuals with an average of 5.3 connections each at the first exam, to 3500 individuals with 2.8 connections on average at the seventh exam. Summary statistics are presented in the supplement (Table S1). These changes in population size and average degree occur because individuals may die or drop out of the study but new individuals are not added. The network is approximately Poisson distributed (see Figure 2), although with some subjects having no connections. The transitivity is consistent over time at approximately 0.64. While neighbors were included as contacts in the study, like Fowler and Christakis [20] we find no significant trends when including neighbors, and so did not include these contacts. For friendships, we only consider the contacts of an individual to be those other individuals whom they nominated (other relationships are all mutual), and so the network is directional. PPT PowerPoint slide

PowerPoint slide PNG larger image

larger image TIFF original image Download: Figure 2. The degree distribution of the Framingham Heart Study Network. The degree distribution of the Framingham Heart Study social network at the most recent exam (7) considered in this study. Connections include friends, family and coworkers. The average degree is around k = 3 and the transitivity is = 0.64 (the ratio of triangles to triples). https://doi.org/10.1371/journal.pcbi.1000968.g002 The results of infectiousness analysis for the spread of obesity between exams 4 and 5 are shown in Figure 3 as an example. Consistent with the SISa model formulation, we find a significant positive correlation between the probability of transitioning from ‘not obese’ to ‘obese’ and the number of ‘obese’ contacts (Figure 3A, coeff = 0.016, p = 0.0001), and no significant relationship between the transition from ‘obese’ to ‘not obese’ and the number of ‘not obese’ contacts (Figure 3D, coeff = 0.006, p = 0.15). Additionally we find no significant relationship between the probability of transitioning from ‘not obese’ to obese and the number of ‘not obese’ contacts (Figure 3B, coeff = −0.0005, p = 0.75), or the probability of transitioning from ‘obese’ to ‘not obese’ and the number of obese contacts (Figure 3C, coeff = −0.002, p = 0.85). The same analysis was repeated for each interval between sequential exams and very similar results were found. The full results from the regression analysis are presented in the supplement (Table S2). This suggests that obesity can indeed be modeled as an infectious process in the SISa framework, with ‘not obese’ susceptibles becoming ‘obese’ infecteds, and transmitting obesity to other susceptibles. The parameters for the SISa model can be calculated from the transition probabilities mentioned earlier, by dividing slope and intercept values by , the average time between exams. These values are reported for each exam in Figure 4, and the values at the latest exam interval are summarized in Table 1. For most recent exam, the transmission rate, , is found to be /year. The spontaneous transmission parameter is found to be /year. The recovery parameter is found to be /year. From these SISa model parameters, other values of interest can be calculated. The ‘average lifetime’ of a state is the average length of time and individual spends in this state before recovering, which was found to be 24 years for this time period. The ‘influence’ of a state is the cumulative probability that the infection will be passed from an infected to a susceptible connection before the infected individual recovers, and is observed here to be 13 . The ‘cycle length’ is the average length of time between spontaneous infections, and is 56 years. The basic reproductive ratio is approximately 0.35, which implies that without spontaneous appearance, the obesity epidemic would not be self-sustaining based on transmission alone. However this calculation is an approximation since uses the formula for a population that is well-mixed but only effectively contacting a fraction of the total population at each time ( contacts), so does not factor in fixed network structure (there is no analytic formula for this situation). We observed a correlation in the positioning of obese and non-obese individuals of = 1.3 and = 0.9. PPT PowerPoint slide

PowerPoint slide PNG larger image

larger image TIFF original image Download: Figure 3. Evidence for disease-like spread of obesity. Obesity behaves like a disease agent, infecting those in a susceptible ‘not obese’ state. The probability of transitioning from ‘not obese’ to ‘obese’ increases in the number of ‘obese’ contacts (A), and doesn't depend on the number of ‘not obese’ contacts (B). Conversely, the probability of recovering to the ‘not obese’ state does not depend on the number of ‘not obese’ contacts (D) or the ‘obese’ contacts (C)). Labels above points on plot are the number of observations averaged into that data point, and error bars are the standard error of the proportion. https://doi.org/10.1371/journal.pcbi.1000968.g003 PPT PowerPoint slide

PowerPoint slide PNG larger image

larger image TIFF original image Download: Figure 4. Change in observed parameters over time. Parameter measurements for obesity from each set of consecutive exams. Data point at exam N represents the value for the transition from exam N to N+1. Error bars are 95 confidence intervals on measurements from regression of transition probability versus number of contacts of a certain type. (A) Contact-independent rates. The rate of recovery ( ) appears to be constant within the margins of error throughout the study while the rate of automatic infection ( ) appears to increase between exams 1 and 3, then stay constant. (B) The contact-dependent transmission rate ( ) appears to increase over time. https://doi.org/10.1371/journal.pcbi.1000968.g004 PPT PowerPoint slide

PowerPoint slide PNG larger image

larger image TIFF original image Download: Table 1. Parameter estimates for obesity between exams 6 and 7 (1995–2001) using the SISa model framework. https://doi.org/10.1371/journal.pcbi.1000968.t001 Since these rates were measured for 6 different inter-exam transitions over 30 years, we can look at how the value of these rates changes over time. Figure 4 shows the measured automatic infection (a), transmission ( ), and recovery rates (g) for each exam interval. Error bars are 95 confidence intervals on measurements from analyses like Figure 3. While the rate of recovery ( ) has remained relatively constant since the 1970s, the rate of spontaneous infection ( ) has steadily increased over time. The transmission rate, , also appears to have increased over time. These trends were tested using weighted regression (to include the different errors for each measurement) and found to be significant for and but constant for . For the rest of the study we used the time-averaged value of , . This suggests that the obesity epidemic may be driven by increasing rates of becoming obese, both spontaneously and transmissively, but not by decreasing rates of losing weight. We also found that both happiness and depression fit the SISa model, both being contagious from a neutral emotional state [18], that smoking cessation, though not smoking itself, also fit, and that both alcohol consumption and abstinence were contagious from the opposite state (data not shown). For all of the above cases, we tested if the transition probability depended instead on the fraction of contacts in a state, instead of the number, and found no significant dependence. We also tested for dependence on other personal attributes such as age, sex and education, and found no dependence in most cases. For obesity, the transition probability from not obese to obese decreased slightly with age (coeff = −0.0012, p = 0.04). Our results show that many models of social influence make assumptions about interpersonal interactions that are not supported by this longitudinal data. One of these assumptions is the ‘majority rules’ interaction, which assumes that people will be most likely to switch to the state most of their contacts are in [40]. Here, transitions depend on the number of contacts, and only certain states (those we class as ‘infectious’) actually influence transitions (in other words, contagion is only in one direction). This has significant effects on the predictions for epidemic progression. For example, ‘majority rules’ models predict 100 infected at steady state, and that weight loss behavior spreads and so an effective intervention is to ‘pin’ certain individuals at low weights. Also, many models assume that the probability of transitioning to a state is zero if no contacts are in that state, but these results show that there is a constant probability of spontaneously becoming ‘infected’. Finally, using this framework, we can get rates for transitions, and hence have an idea for the time-course of the progression, not just the final outcome.