Keywords

1 Introduction

Most workers experience stress sometimes, and when this continues over longer periods of time, people can experience physical consequences of this. Examples include sickness and the feeling of being burn out or emotional exhaustion. In 2017, 15.9% of the Dutch population older than 15 reported burnout-related symptoms [4]. In light of social change and transformations in work situations, interest in this topic has grown. A lot can and is being done to prevent or alleviate burnout syndrome, especially by changing lifestyle or habits. We build on top of existing research by Dujmić et al. [6] by extending their model through adding sleep-related factors. This paper focuses on the optimization of sleep habits as this was found as a protector from burnouts [15].

In contrast to the traditional paradigm for assessing psychological diseases, where these were seen as a latent construct that could be measured by their symptoms, this paper uses a newer paradigm. This newer paradigm defines psychological diseases as the relation or dynamic interplay between symptoms [3]. This fits well to the Network-Oriented Modelling approach described in [23, 24], which is based on temporal-causal network modelling in which networks with dynamic and cyclic causal relations are addressed. This approach can be considered as a branch in the causal modelling area which has a long tradition in AI, e.g. see [11, 12, 18]. This paper aims to help understand the causes, elements, consequences, risk factors and protective factors of burnout syndrome gathered from the literature through network-oriented modelling. The dynamic interaction of these states forms (cyclic) patterns resembling real patterns.

In this study, a non-burnout scenario will be simulated, as well as a burnout scenario and a recovery from burnout scenario. Furthermore, we will show a cyclic pattern with a periodical sleeping pattern. Here, we will make use of a trigger as well (having kids after some point in time) that could potentially disrupt this cyclic pattern.

First, some background literature will be discussed, based on which the network model is constructed, which happens in Sect. 3. Simulations for some example scenarios are shown in Sect. 4, followed by verification of the model by mathematical analysis (Sect. 5) and validation by parameter tuning in Sect. 6. In Sect. 7, the results will be discussed.

2 Background Literature

The classical definition of a burnout, as given by Maslach and Jackson [13], is nowadays still relevant: emotional exhaustion, depersonalization and personal accomplishment are since then still described as the core elements of the burnout syndrome [10]. Maslach created the first measurement instrument for burnouts called the Maslach Burnout Inventory (MBI). She describes various job characteristics that form risk factors for developing a burnout. The most important risk factor is experienced overload, a term describing subjective stress. Long exposure to job-related stress can lead to cynicism and emotional exhaustion, in their turn increasing the chance of a burnout. Other risk factors include job sacrifice, describing how much someone is willing to sacrifice for achieving his or her ideals, and role ambiguity, pointing to the unclarity of what and how much is expected from a worker.

Furthermore, there are job-related factors that either suppress the effects of these risk factors or decrease the core elements of burnout syndrome that are called protective factors. An example of a protective factor is social contact with co-workers, which is found to decrease depersonalization and cynicism [5]. Also, work experience is an important protective factor, since the more experience someone has, the more sense of personal accomplishment one experiences [13]. Experience also lowers the experience of role ambiguity [5]. This study builds on earlier work [6], where similar job-related factors were used, and also some personal characteristics including Neuroticism, Openness and Hardiness. This study aims to extend this research by adding sleep-related factors that can either suppress or enforce burnout causes. Neuroticism is a risk factor associated with higher amounts of stress and experienced overload [9]. Openness, on the other hand, is shown to be negatively correlated with depersonalization and emotional exhaustion [7], and positively correlated with physical exercise [22], and therefore, more of a protective factor. The last personal characteristic we included is hardiness, which is found to protect from the effects of stress, but also is linked to the core elements of burnout [2, 8].

By analysing a questionnaire concerning stress at work, health, sleep and lifestyle factors of 676 employees, [21] identifies four factors as significant burnout predictors: work demands, thoughts of work during leisure time, sleep quality and getting too little sleep (less than six hours). The latter was identified as the main risk factor for clinical burnout. Söderström et al. [21] concludes that getting insufficient sleep and having difficulties detaching from thoughts of work during leisure time are stronger predictors of burnout syndrome than stressful work demands, highlighting the importance of recovery from stress—and not that much stress itself—in the process of developing a burnout. As described by Miró et al. [15], sleep quality, next to job-related factors, is a significant predictor of a burnout. Their research showed a higher impact on emotional exhaustion than job demands in our study described as ‘feeling of charged work’. Also, sleep quality interacts with other job-related factors. Furthermore, Rosen et al. [20] showed that not only sleep quality but also sleep quantity has a serious impact on the development of burnout. Analogically, whether a person has uniform working hours plays an important role in merely sleep quantity. Akerstedt and Wright [1] confirmed this and more importantly showed the impact of habitual sleep efficiency, a term to describe the percentage of time in bed that a person is asleep. Pagnin et al. [17] showed that daytime dysfunction is an important predictor for emotional exhaustion and cynicism. A meta-analysis by Pilcher and Huffcutt [19] showed that lack of sleep significantly impairs human functioning during daytime activities. Obviously, earlier named sleep factors have an influence on daytime dysfunction. To complete the sleep-related factors, sleeping pill intake and caffeine intake were added to the model. Sleeping pill intake has a positive effect on daytime dysfunction [25] and may vary depending on the sleep quality and sleep quantity. McGeary et al. [14] also showed a relation between caffeine intake and burnout, while caffeine intake can also reduce daytime dysfunction. These factors can result in a cyclic pattern when affecting other factors.

3 The Designed Network Model

Based on the literature discussed in the previous section, in this section, we describe the temporal-causal network model we used. This model is based on the Network-Oriented Modelling approach described in [23, 24] and was implemented using the software environment described in [16]. Table 1 provides a concise overview of a temporal-causal network model in general. The differential equations in the last row in Table 2 can be used for simulation and mathematical analysis.

Table 1 Representations of a temporal-causal network; adopted from [24]
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Table 2 States used in the model with their combination functions and their parameters
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They can also be written in differential equation format:

$$\begin{aligned} Y(t +\Delta t) & = Y(t) +\varvec{\eta}_{Y} \\ & \quad [{\mathbf{c}}_{Y} ({\varvec{\upomega}}_{{X_{1} ,Y}} X_{1} \left( t \right), \ldots ,\varvec{\omega}_{{X_{k} ,Y}} X_{k} \left( t \right)) - Y\left( t \right)]\Delta t \\ \end{aligned}$$
(1)
$${\mathbf{d}}Y\left( t \right)/{\mathbf{d}}t =\varvec{\eta}_{Y} [{\mathbf{c}}_{Y} (\varvec{\omega}_{{X_{1} ,Y}} X_{1} \left( t \right), \ldots ,\varvec{\omega}_{{X_{k} ,Y}} X_{k} \left( t \right)) - Y\left( t \right)]$$

Based on the literature—and in particular on the work of [6]—we could identify 29 state variables relevant for a burnout, as shown in Table 2. The table includes the classification of the variables into the risk and protective factors, the elements of the syndrome and the consequent state and also shows the combination functions used and their parameters. Most of the combination functions were chosen as advanced logistic functions:

$${\mathbf{id}}\left( V \right) = V$$
(2)
$${\mathbf{alogistic}}_{{\upsigma,\uptau}} \left( {V_{1} , \ldots ,V_{k} } \right) = \left[ {\frac{1}{{1 + {\text{e}}^{ - \sigma } \left( {V_{1} + \cdots + V_{k - \tau } } \right)}} - \frac{1}{{(1 + {\text{e}}^{\sigma \tau } )}}} \right](1 + {\text{e}}^{{ -\upsigma \uptau }} )$$

The literature suggests many causal relations between the various states in our model, either positive or negative. We captured these relations in the graphical conceptual representation of the model shown in Fig. 1. The strength of these causal relations is represented by assigned connection weight values, see Table 3.

Fig. 1
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Graphical conceptual representation of the temporal-causal network model

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Table 3 Connection weights
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The green lines represent a high positive effect and the yellow line a slight positive effect. The red, orange and cyan lines show a negative effect, ranging from a high effect (red) to a slight effect (cyan). Note that X27 and X28 are external factors which will be explained below.

Examples of the difference and differential equations in the model are following:

Examples of a states using the identity (3) and the logistic (4) combination function

$${\text{JS}}(t + \Delta t) = {\text{JS}}\left( t \right) + \eta_{\text{JS}} [\omega_{\text{FW,JS}} {\text{FW}}\left( t \right){-}{\text{JS}}\left( t \right)]\Delta t$$
(3)
$$\frac{{{\text{dJS}}\left( t \right)}}{{{\text{d}}t}} = \eta_{\text{JS}} [\omega_{\text{FW,JS}} {\text{FW}}\left( t \right){-}{\text{JS}}\left( t \right)]$$
$$\begin{aligned} {\text{JD}}(t + \Delta t) & = {\text{JD}}\left( t \right) \\ & \quad + \eta_{\text{JD}} [{\mathbf{alogistic}}_{{\upsigma,\uptau}} (\omega_{\text{CY,JD}} {\text{CY}}\left( t \right),\omega_{\text{SC,JD}} {\text{SC}}\left( t \right)){-}{\text{JD}}\left( t \right)]\,\Delta t \\ \frac{{{\text{dJD}}\left( t \right)}}{{{\text{d}}t}} & = \eta_{\text{JD}} [{\mathbf{alogistic}}_{{\upsigma,\uptau}} (\omega_{\text{CY,JD}} {\text{CY}}\left( t \right),\omega_{\text{SC,JD}} {\text{SC}}\left( t \right)){-}{\text{JD}}\left( t \right)] \\ \end{aligned}$$
(4)

4 Simulations for Three Example Scenarios

To validate our model against typical burnout patterns described in the literature, we created three example scenarios and simulated them using the dedicated software environment described in [16]. First, Scenario 1 in which no burnout occurs, and next Scenario 2 in which burnout does occur. For Scenario 1, we expected a stable situation, where a person has high enough protective factors and low enough risk factors, such that the burnout elements diminish and all states will move into equilibrium. For the burnout Scenario 2, we expected that high-risk factors would overwhelm low protective factors, such that the burnout elements and its consequences would increase over time. Suitable initial values were assigned as shown in Table 4. For instance, a situation where a burnout occurs is probably accompanied with a low amount of sleep and a high daytime dysfunction in contrast to a no burnout scenario. In addition, we added Scenario 3 of ‘recovery’, namely where a person would experience some burnout elements, but then recovers and state values of burnout elements would slowly fade away. To model this scenario, we created a mix of high- and low-risk factors—as also shown in Table 4.

Table 4 Initial values for the three different scenarios
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In Scenario 1, there is not one sudden change in state values to be observed, as the protective factors continue to increase (if not constant), while the opposite holds true for the risk factors. Thus, the burnout elements drop even further until an equilibrium situation is reached. Scenario 2 displays a situation where a person gradually develops a burnout. Low protective factors like work experience, openness and social contact with co-workers are not enough to diminish the high-risk factors like daytime dysfunction, neuroticism and with feeling charged work. Thus, experienced overload increases and consequently with it the burnout elements emotional exhaustion and cynicism, while the third burnout element personal accomplishment is decreasing to zero. Consequently, job resignation and physical health problems both increase. Sleep quantity increases first, as the high daytime dysfunction is leading to an increase in sleeping pill intake, until daytime dysfunction and high experienced overload peak, causing the sleep quantity to settle on a lower level.

Scenario 3 shows a person who is starting to experience a burnout, but then it fades away due to high enough protective factors. Burnout elements and its consequences, like job detachment, are all high in the beginning, while sleep quality is low. In addition, protective factors like working experience and hardiness are high, while some risk factors like sleep deprivation and with feeling charged work are low. The combination of low-risk factors and high protective factors is enough for the burnout symptoms to lower over time, until a stable no burnout scenario is reached (Figs. 2 and 3).

Fig. 2
figure 2

Simulation of Scenario 1 (left, no burnout) and 2 (right, burnout)

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Fig. 3
figure 3

Simulation of Scenario 3: recovery from burnout

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5 Verification of the Model by Mathematical Analysis

For verification, we analysed the stationary points and equilibria occurring in the model. A stationary point of a state Y at time t occurs when dY(t)/dt = 0. The network model is in equilibrium at t when all states have a stationary point at t. As described in Sect. 3 Eq. (1) in a temporal-causal network model, the differential equation for all states is dY(t)/dt = ηY [aggimpactY(t) – Y(t)]. As all speed factors ηY in the model are nonzero, all stationary points must follow the criterion aggimpactY(t) = Y(t), also formulated as: in a temporal-causal network model, there is a stationary point for state Y at t if and only if ηY = 0 or cY(ωX1,YX1(t), …, ωXk,YXk(t)) = Y(t). Using this criterion, first we looked at the burnout Scenario 1 from above and identified a stationary point for emotional exhaustion at t = 3.3. The aggregated impact, other states have on emotional exhaustion, is modelled with an advanced logistic function with steepness σ = 10 and threshold τ = 0.5. Openness and experienced overload are the two states affecting emotional exhaustion with connection weights of −0.5 and 1, respectively. The values for emotional exhaustion at time t = 3.3 for the stationary point and at time t = 100 for the equilibrium are 0.25301 and 0.98177, respectively. In addition, the values for experienced overload are 0.49759 resp. 0.99997, while openness has a constant value of 0.2. We used the values for openness and experienced overload to compute the aggregated impact they have on emotional exhaustion, as shown in Table 6. We did this also with the stationary points and equilibria occurring for sleep quantity and drug use. The state values and aggregated impacts show little differences, which add to confidence that the model does what is expected (Table 5).

Table 5 Outcomes of the verification
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6 Validation of the Model by Parameter Tuning

For further validation of the model, we used simulated annealing based on acquired data for parameter tuning. For this, we evaluated the prevailing literature regarding the relation of daytime dysfunction and quality and quantity of sleep (e.g. [1, 15, 17, 20, 21]), as well as the use of caffeine and sleeping pills to overcome daytime dysfunction (e.g. [14, 15]). Through these scientifically based relations, we were able to create expected patterns of how those factors would interact. Based on that, we could create data points meeting those expected patterns, as shown in Table 6.

Table 6 Expected pattern of sleeping factors
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Over time, we expected a sequential pattern, where high daytime dysfunction would increase sleeping pill intake, leading to a subsequent rise in sleeping quantity. A rise in sleeping quantity in turn starts to have an effect on sleep quality and daytime dysfunction. With a lowered daytime dysfunction, the sleeping pill intake decreases, until sleep quantity decreases again and the causal chain begins all over again. We started to create this pattern for a person with high daytime dysfunction. For a high daytime dysfunction (0.92), we could expect an equally low sleep quality (0.07). For a sleep-deprived person, we expected a higher resistance using sleeping pills in comparison with caffeine intake thus the higher value for caffeine than for sleeping pill intake. The combination of high daytime dysfunction (0.92) and relatively high sleeping pill intake (0.74) should result in a medium sleep quantity (0.44). With a decreasing daytime dysfunction and recovering sleep quality, we expected the sleeping pill intake to decrease faster than the caffeine intake (e.g. time 10–20). Likewise, as daytime dysfunction increases again, sleeping pills should show a higher increase used over time, as they are more addictive than caffeine (e.g. time 40–50). With the generated data obtained from interpolating our expected values, we could compare these to our model. Indeed, parameter tuning gave a higher steepness as well as a higher threshold for sleeping pill intake. The root mean square error (RMS) for the five selected factors is 0.028758, which is relatively low. Perhaps, this may be because our estimation of empirical values was partly biased by what we knew already about typical model patterns. With our tuned model, we validated our model against expected patterns based on personality and lifestyle factors. At first, our aim is to model a high demanding job situation, including a low value of personal accomplishment and high values of cynicism and emotional exhaustion. Low protective factors and high-risk factors lead to a scenario where a burnout occurs. In addition, through the high experienced overload and low physical exercise, the sleeping quantity decreases. This turns into a rise in daytime dysfunction, which is causing a higher intake of sleeping pills. In turn, the sleep quantity rises, until daytime dysfunction lowers and consequently the intake of sleeping pills. Thus, it causes daytime dysfunction to rise again and the pattern repeats itself. Simultaneously, personal health problems fluctuate with the sleeping pill intake (Fig. 4).

Fig. 4
figure 4

Burnout Scenario 1 with periodic sleeping pattern (left) and having kids after some point in time lower the sleep quantity, thus breaking the cyclic pattern (right)

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After the model settles down to its equilibria, we introduce an external state variable with impact on having kids at around t = 210 (150 + 60), which in turn can negatively affect the amount of sleep. We implemented this via introducing the external factor EXT, which has an impact on having kids HK. This external factor EXT was modelled using a connection to itself and with an advanced logistic sum combination function with σ = 18, τ = 0.2 and speed 0.04; the state HK has σ = 50, τ = 0.8 and speed 1. Thus, the external factor EXT builds up very slowly and has very little impact on having kids HK, until the threshold is reached (at birth) and the state value of having kids HK changes quite abruptly. In this scenario, it is enough that even an increased sleeping pill intake can no longer match the negative effects on sleeping quantity, which results in increase of daytime dysfunction. This in turn causes sleep quantity and quality to fall to low equilibrium values.

7 Discussion

In this study, we introduced a temporal-causal network model for a burnout in relation to sleep. The Network-Oriented Modelling approach described in [23, 24] was used, and for implementation the dedicated software environment is described in [16]. The modelling approach showed the impact of different lifestyle, personal and job factors on the development of a burnout. This model can be the basis for different types of simulations. For instance, an agent-based model can be used to schedule night shifts in order to preserve the needed recovery. Also, our model can be used to simulate the effects of certain changes in lifestyle on the development of burnout, especially when even more states are added to resemble the real-world complexity.

For validity, it was critical to implement both risk and protective factors. To analyse computationally their roles in development and recovery, we designed different scenarios, such as the one of a burnout and a non-burnout, and a scenario where a burnout occurs and a periodic pattern between sleep-related factors arises. It showed that a small increase in sleep disturbance in an already demanding situation can cause a non-recoverable downwards movement. Unfortunately, there was no numerical empirical data available to test these patterns in more detail. For example, it is unclear to extract from the literature how strong and fast certain variables relate. Consequently, this gives room for improvement on our model regarding how the relations of the variables vary in type, speed and weight.