Modelling population responses to workplace minimum dietary standards introduced as workers return after social lockdowns

Households were generated within the model and populated with adults with a given employment status and a number of children (Table 1). The household population defined one social network and eating group for an agent (i.e. person) and a second social network was described by workplace (adults) or school (children). Workplaces were created in proportion to the number of households and stratified by their number of employees (big, medium or small; Table 1), which defined the total population size in the workplace. In order that the model is situated with plausible socio-demographic structure, the data were based on a real city, in this case Aberdeen, Scotland, but this model could be applied to any location.

The model used meal-based time steps (i.e. breakfast, lunch, dinner) with three time-steps per day. For breakfasts, dinners and all weekend meals, agents were all assumed to eat within their household group. For workplace weekday lunches, workers ate in a group that was uniformly randomly sampled from co-workers at the same workplace and children similarly ate in randomised networks within their school. At each day within the model, each workplace/school had a random daily menu of food options, uniformly sampled from those that met the minimum dietary standards. Agents therefore ate with their home network at the start of each day, would take those preferences towards their food choices into the workplaces (as their personal norm), update their preference through interaction with their workplace/school social network and return home with the updated personal norm to again interact with their home social network. In households that had adults in different workplaces and children at school, this would mean multiple sources of influence were brought home for the evening meal choice and in workplaces, heterogeneous households would mix.

The process of how agents select diets is illustrated in Fig. 1. In summary, agents follow a series of rules to select meals:

or

At each meal, every individual had an internal preference that was unaffected by co-eaters, but determined by the personal norm. The personal norms for each agent was defined by an individuals’ diet behaviours built up over time and akin to their habitual intake. Here, a personal norm was described by a random normal distribution centred on their running mean of preceding choices (default to 45, approximately two weeks of meals) and with a standard deviation that was assigned at initialisation (see below). The internal preference was a random draw from the personal norm. For agents who ate on their own, for example they lived alone and did not work, their final meal selection was the same as their internal preference, i.e. their personal norm was unchanged.

A descriptive group norm [19], the observed shared diet behaviour of a group of individuals eating together, was defined in two ways depending on context: in the household (for breakfast and dinner or lunches at weekends) the mean of the internal preferences from each household member was calculated and was then assigned to all household members as their final preference assuming that they all eat the same meal. The shared norm was therefore the average of household members’ preferred meal choices. For workplace or school lunches, the group norm was characterised by a random normal distribution centred on the mean and standard deviation of co-eaters’ internal preferences. For each agent, a weighted mixture of the group and personal norms was estimated to simulate norm matching [7, 20] and this mixture distribution was sampled to produce a final meal preference.

The meal chosen was then the meal from the daily menu of the workplace/school, all choices of which had to meet the minimum dietary standards, or from an unconstrained list in the case of home meals, that most closely matched the final preference. An agent’s running average was updated with the chosen meal and this became the basis for the internal choice in the next (meal) time step.

In addition to the norm-based theory underpinning behaviours [21], empirical data were used to ground the model. Initial values are shown in Table 1.

The population structure was based on the tangible example of a medium sized UK city, Aberdeen, for which there was detailed census data (2011). For computational constraints, the model was populated with 1,000 households (approximately 1% of the number of households in Aberdeen). To illustrate food choices, we based meal selection on a diet quality index (DQI), which reflects the whole diet intake of macronutrients and food groups that is scaled zero to 100 (higher values indicative of higher diet quality) [22]. To score modelled meals, we sampled from the DQI calculated for observed whole diets reported from years 1 – 4 of the self-reported four-day diaries in the National Diet and Nutrition Survey rolling program (NDNS) [23], during which a nationally representative sample of 1000 individuals per year record a diet diary. The NDNS is cross-sectional and the DQI applies to the whole diet rather than individual meals or days and therefore does not have temporal variation per person. To describe how variable diet choices were per agent we supplemented this with analysis of longitudinal sample of 1988 Scottish households from the Kantar WorldPanel [24] to estimate the week-to-week DQI standard deviation (calculated over 100 weeks) of purchased food. The standard deviation of the per person DQI, i.e. household DQI divided by the number of occupants, was closely approximated by a normal distribution (mean 13.5, SD 2.5; Additional File 1) from which agents were assigned a random value at initialisation to define the variability of their unconstrained preference. We additionally assumed that agents differ in their degree of norm matching and we operationalised this with a random triangular distribution (from zero to one and with a peak at 0.39 following [25]) and assumed that this value remained constant. Sensitivity to changing the peak of the weighting distribution was evaluated (Additional file 2).

Models were run in which the minimum dietary standard was increased from zero to 80. The daily menu in schools and workplaces therefore ranged from the minimum standard to 100, but from zero to 100 for other meals (i.e. at home). Minimum standards were imposed either universally in all workplaces and schools or in all schools and workplaces of different sizes separately.

The model ran according to a narrative of UK COVID-19 restrictions, from pre-pandemic, through restrictions to easing with a gradual return to work where minimum dietary standards had been introduced for all meals served in workplace canteens: (i) time-steps zero to 100 (~ 33 days) of status quo, i.e. no minimum standards; (ii) time-steps 101 to 200 in which all adult agents are restricted to eat within their household group (i.e. enforced working-from-home), but that children ate lunch at school and were exposed to school-based minimum dietary standards (if any); (iii) time-steps 201–500 during which (a) new minimum standards were imposed in some workplaces and (b) a constant proportion of workers, uniformly sampled at random, stay at home each day (i.e. a gradual return to workplaces). In the first experiments, minimum dietary standards to mimic introducing rules about the type of food served in work or school settings were included. For illustration, a DQI of 60 was imposed which represents an increase of approximately 50% in the mean of the observed DQI from the NDNS data (mean 37.4, SD 18.7). Given that a DQI of 100 represents recommended whole diet intakes, the minimum score is a relatively modest standard to impose on individual meal and sensitivity analyses varying this value showed the same qualitative pattern but absolute differences in the population average. For each parameter combination, 20 iterations were run to describe stochastic variability and although this was a relatively low number of iterations the simulation runs were very similar (Additional File 3).

The model was written in Netlogo [26] and analysed in R [27].

The first scenario was to introduce minimum dietary standards in the form of a daily restricted menu in workplaces and schools that had to meet or exceed some threshold diet quality. Figure 2 shows the responses of the adult population to increasing the minimum standard. While minimum standards were lower than or close to 38, the median of the starting distribution for the adult diet index, there was little impact on the median of the population. However, as the minimum diet standard was increased, the median diet quality of the population also approximately linearly increased (linear regression, mean effect 0.48 [95% CI 0.34, 0.62] per 1 point increase in minimum standards, p < 0.001). Given that during the first 200 time steps, minimum standards were only assumed to be present in schools and then standards were introduced into workplaces as well, there were two distinct steps in the adult dietary index when adults were exposed to the new standards. The distribution the population also became increasingly skewed as the majority, but not all, of the population regressed toward the minimum standard.

Figure 3 shows the distribution of adult dietary scores if minimum standards are introduced in different settings. The highest median scores are observed when all workplaces and schools have minimum standards. Minimum standards in big or medium sized workplaces or in schools had similar adult dietary scores, but standards in only small workplaces had little impact in any household. In this case there were fewer people to mix with and therefore be influenced by.

Figure 4 shows the results from a single iteration of the model to illustrate the trajectory of every adult from the modelled population and assuming minimum standards of 60 (in both workplaces and schools). Model iterations were highly consistent (Additional File 2) and this single iteration is representative of the patterns observed. Depending on whether individuals started below, around or above the population average, they increased, stayed approximately the same or decreased toward the population average. However, a sizeable minority of individuals who are not exposed to the intervention either through work or children at school do not converge on the population average hence the increasing breadth of the 95% confidence interval seen in Fig. 2.

Figure 4 also contrasts two scenarios, with or without a return to work after 200 time steps. When workers return to work they mixed with one another and there was rapid convergence toward the minimum standard that resulted in a narrow (albeit skewed) distribution. If workers remain isolated (bottom row of Fig. 4) and only ate within their home group, they tend to have an approximately constant diet and did not converge on a shared norm. A secondary consequence was that when workers were isolated they were not exposed to the intervention except through children attending school and the population average was lower (mean adult diet index 63 with no isolation versus 53 with all workers isolated). The more workers who stayed at home the more attenuated the effect of the intervention (Fig. 5). There was an approximately linear trend in the mean effect of worker isolation, with a -2.36 point reduction in diet quality (95% CI -2.40, -2.34) per additional 20% workers isolated.

Figure 6 illustrates adult diet index trajectories from one iteration of the model, but stratified by the household (whether there are any working adults or children in the house) and the size of the workplace the worker in the model attends. Adults with children increased their diet standard faster than adults without children (the mean effect of the interaction between child presence and time for the first 300 days, 0.077 diet quality, 95%CI 0.059, 0.095, but thereafter the interaction was non-significant, -0.005, 95%CI -0.014, 0.003) because children are exposed to minimum standards from time step zero and they bring the updated norms back into the household, creating a positive ‘spillover’ of diet norms from school to home.

Assuming minimum standards in workplaces (from t = 200) and schools (from t = 0) and no working from home, adults who were exposed to minimum standards through children before those without children, achieved similar though significantly different, mean diet quality index scores at the end of the simulation (at 500 time steps mean ± SD, 67.0 ± 4.7 for adults with children in the household versus 63.1 ± 11.0 for adults without children, T test p < 0.01). At the end of the simulation, the difference between adult diet quality index scores for workers were significantly higher and less variable than for non-working adults (66.7 ± 5.4 for adult workers and 48.9 ± 15.4 for non-working adults, T test p < 0.01). However, the greatest difference was that between working adults with children in the household (67.2 ± 4.2) and adults who neither worked nor had children (46.6 ± 15.0) and it was notably more variable in addition to the difference in the mean.

Figure 6 also indicates the weight given to modelling diet choice on the group norm versus the personal norm (Pearson’s correlation 0.02). Strongly polarising the probability to either the personal or group norms had a small impact on the adult diet quality index scores (decreasing variability around the mean) but no impact on the correlation (Additional File 3).