An Adaptive Network Model for Burnout and Dreaming

Abstract

As burnouts grow increasingly common, the necessity for a model describing burnout dynamics becomes increasingly apparent. The model discussed in this paper builds forth on previous research by adding dreams, a component that has been shown to have an adaptive regulating effect on emotions. The proposed model is a first-order adaptive temporal-causal network model, incorporating emotions, exercise, sleep, and dreams. The model was validated against given patterns found in the empirical literature and it may be used to gain a better understanding of burnout dynamics.

Full text

An Adaptive Network Model for
Burnout and Dreaming
Mathijs Maijer1, Esra Solak1, Jan Treur2
1University of Amsterdam, Computational Science
2Vrije Universiteit Amsterdam, Social AI Group
m.f.maijer@gmail.com s.3.solak@gmail.com j.treur@vu.nl
Abstract. As burnouts grow increasingly common, the necessity for a model de-
scribing burnout dynamics becomes increasingly apparent. The model discussed
in this paper builds forth on previous research by adding dreams, a component
that has been shown to have an adaptive regulating effect on emotions. The pro-
posed model is a first-order adaptive temporal-causal network model, incorpo-
rating emotions, exercise, sleep, and dreams. The model was validated against
given patterns found in empirical literature and it may be used to gain a better
understanding of burnout dynamics.
1 Introduction
Burnouts have grown more common and it is becoming an important issue in society
nowadays. People are complaining more often about demanding jobs and the toll they
take. A burnout is seen as a buildup of long-term unresolved work-related stress. Re-
cently, the World Health Organization has classified an occupational burnout as a syn-
drome [1]. There may be multiple causes for the development of this syndrome, but
according to the WHO, it can arise from a failure to manage chronic work-related stress.
This can cause feelings of energy depletion, exhaustion, job detachment, negative feel-
ings and cynicism towards the job, and reduced professional efficacy [1]. The number
of people complaining about burnout related symptoms has increased over time and it
is rising fast. In 2015, 13 percent of the Dutch employees mentioned burnout symptoms,
this figure has risen to 16 percent by 2017 [2, 3]. Around 20 percent of employees aged
between 25 and 35 have mentioned burnout symptoms in the Netherlands, which is
certainly a concerning issue.
Due to the increase in burnout complaints and the severity of the issue, it has
become more important to not only analyse the causes of burnouts, but also how to
prevent, avoid, and if possible, cure them. A few possibilities to fight against burnouts
may be lifestyle or habit changes. This paper uses previous research [4][5], to build
forth on the already created temporal-causal network models that describe the burnout
syndrome as a dynamic interplay between symptoms [6]. In [4], the initial model was
created and the effects of physical exercise were analysed, in [5] sleep factors were
added to improve the model. This paper adds relevant dream components as described
in [7] and also makes the model adaptive, resulting in a first-order adaptive temporal-
causal network model. The main modelling approach is inspired by [8].

2
The aim is to gain a better understanding of the development of burnouts and to
create a more realistic model that can be used in real-life scenarios. In Section 2, a brief
overview of the relevant background knowledge will be provided; in Section 3, the
network-oriented modelling approach will be explained in some detail. In Section 4,
the designed adaptive network model will be described. Multiple simulations will be
given in Section 5. Section 6 and Section 7 will respectively address empirical and
mathematical validation of the model. Finally, a discussion concludes the paper.
2 Theoretical Background
This paper assumes the classic definition of the burnout as mentioned in [9]. It describes
the symptoms of emotional exhaustion, a decline in experiencing personal accomplish-
ment, and a sense of depersonalization. These symptoms are also described in the WHO
classification of a burnout [1]. The main idea behind the definition of Maslach, was to
invent a measurement instrument for burnouts [9]. Various components are mentioned
that interact together to form a burnout. The most important components are described
as risk factors and suppressive factors, also called protective factors. Among the risk
factors are subjective stress, job ambiguity, work pressure, thoughts of work during
leisure time, the amount of sleep, and the quality of sleep. Protective factors are, for
example, confidence, or the amount of physical exercise [4] and sleep [5]. Factors that
influence the progression or development of burnout symptoms are influenced by per-
sonal characteristics [10]. For example, neuroticism has shown a strong correlation with
experiencing stress. Next to this, openness has been shown to be negatively correlated
with depersonalization and emotional exhaustion [11]. Because of the link between
openness and physical exercise [12], previous research has analyzed the effects of phys-
ical exercise on the dynamics of a burnout [4]. In [5], the relation between sleep and
burnout dynamics is analysed. This is partially done by analysing the results of a ques-
tionnaire which showed that insufficient sleep can be used as a predictive factor for
clinical burnout [13]. A noteworthy finding is that the amount of sleep is a better pre-
dictor for a clinical burnout than the amount of stress someone experiences at work.
Next to sleep, dreams have been found to have a regulating effect on some emo-
tions [7, 15, 16, 17] which is considered a form of internal simulation. The internal
simulation consists of activation of memory elements, which are sensory representa-
tions in relation to emotions. Dream episodes occur after competing, which will activate
different sensory representations (e.g., images) during dreams. The level of how much
the feeling states and sensory representations are activated is controlled by different
control states. In [7], an adaptive temporal-causal network model is introduced to model
dream dynamics that shows a form of adaptiveness called fear extinction [17]. Here
emotion regulation is included of which the connections become stronger as they are
used more [18], according to the principle of hebbian learning. Fig. 1 shows a concep-
tual representation of part of the adaptive temporal-causal network model that is pre-
sented in [7]. Five states are shown, a sensory representation state, an emotion regula-
tion control state, a dream episode state, a feeling state and a preparation for a bodily

3
response state. The red arrows indicate inhibition, or a negative impact, and the black
and blue arrows indicate a positive impact, where the green arrows are adaptive.
Fig. 1. Conceptual representation of part of an adaptive temporal-causal network model
for dream dynamics
3 Network-Oriented Modelling
The temporal-causal network model presented here was designed using a network-ori-
ented modelling approach that is described in [7] and [8]. Network-Oriented Modelling
uses nodes and vertices, which are the connections between nodes. Nodes are states
with values that vary over time, while the connections can be seen as the causal rela-
tionships between these nodes. For an adaptive network model, besides the states also
the causal relationships can change over time. Table 1 summarises the main concepts
of network oriented modelling. The connections indicate the impact that states have on
each other. Every connection has a connection weight, which is a numerical value in-
dicating the connection strength. The connections and their weights define the net-
work’s connectivity characteristics.
Next to this, every state has a combination functions that describes the manner in
which the incoming impacts per connection are combined to form an aggregated im-
pact. This defines the network’s aggregation characteristics. A combination function
can be a basic combination function from the available Combination Function Library
or a weighted average of a number of such basic combination functions. Which combi-
nation function is used depends on the application and can also be node-specific. To
define the network’s timing characteristics, every state has a speed factor that deter-
mines how fast a state changes because of its received causal impact.
Table 1. An overview of the concepts in the conceptual component of temporal-causal networks
Concepts
Notation
Explanation
States and
connections
X,Y
X→Y
Denotes the nodes and edges in the conceptual represen-
tation of a network.
Connection weights
X,Y
A connection between states X and Y has a corresponding
connection weight. In most cases X,Y [-1,1].
Aggregating multiple
impacts on a state
cY(..)
Each state has a combination function and is responsible
for combining causal impacts of all states connected to Y
on that same state.
Timing of the effect of
causal impact
Y
The speed factor determines how fast a state is changed
by any causal impact. In most cases: Y[0,1].
psb
cssk,b
srssk
dessk
fsb

4
The numerical representation derived from the network characteristics is summa-
rised in Table 2. The last row of this Table 2, shows the difference equation. Adaptive
networks are networks for which some of the characteristics X,Y cY(..), Y change over
time. To model this, extra states are added that represent the adaptive characteristics.
For example, for an adaptive connection weight X,Y a new state WX,Y is added (called a
reification state or adaptation state for X,Y) representing the dynamic value of X,Y.
Table 3 shows an overview of the combination functions used in the designed model.
The first is the identity function id(.), which is commonly used when a state only has
one incoming connection.
Table 2. Numerical representations of temporal-causal networks
Concepts
Notation
Explanation
State value at time t
Y(t)
For every time t a state Y has a
value in [0,1].
Single causal im-
pact
impactX,Y(t)
= X,Y X(t)
At any time t a state X (if con-
nected to Y) impacts Y through
a connection weight X,Y.
Aggregating multi-
ple impacts on a
state
aggimpactY(t)
= cY(impactX1,Y(t),…, impactXk,Y(t))
= cY(X1,YX1(t), …, Xk,YXk(t))
The combination function cY
determines the aggregated
causal impact of states Xi on Y.
Timing of the effect
of causal impact
Y(t+t) = Y(t) +
Y [aggimpactY(t) - Y(t)] t
= Y(t) +
Y [cY(X1,YX1(t), …, Xk,YXk(t)) - Y(t)] t
The speed factor Ydetermines
how fast a state Y is changed
by the aggregated causal im-
pact of states Xi
The advanced logistic sum function alogistic,(..) is used to aggregate impact for
each state that has multiple incoming connections; it has as parameters steepness  and
threshold . The combination function hebb(..) is used for adaptation states WX,Y, rep-
resenting the adaptive value of a connection weight. It has one parameter μ, which is
the persistence of the state. In all formulaTable 3 the variables V1,...,Vk are used for
incmimng single impacts, and W for the value of the connection weight reification state.
Table 3. Overview of the combination functions used
Combination function
Description
Formula cY(V1,...,Vk) =
id(.)
Identity
V
alogisticσ,(..)
Advanced logistic sum


  
(1+e-στ)
hebbμ(..)
Hebbian learning
V1V2(1-W)+μW
4 Modeling Adaptive Burnout Dynamics with Dreams
This section describes the details of the designed adaptive network model. The states
shown in the model are mainly based on the literature mentioned in Section 2, specifi-
cally [4] and [5]. Table 4 shows the different states that are used in the model, as well
as their respective types. There are 5 different state types:

5
Table 4. The states used in the model and their respective types
State
Abbr.
Description
Type
X1
CO
Confidence
Protective
X2
OP
Openness
Protective
X3
PE
Physical exercise
Protective
X4
PA
Personal accomplishment
Protective / Consequent
X5
NR
Night rest
Protective / Consequent
X6
CW
Charged work
Risk
X7
JA
Job ambiguity
Risk
X8
JS
Job satisfaction
Protective / Consequent
X9
NE
Neuroticism
Risk / Consequent
X10
SC
Social contact
Protective
X11
EE
Emotional exhaustion
Burnout element
X12
CY
Cynicism
Burnout element
X13
JP
Job performance
Consequent
X14
JD
Job detachment
Consequent
X15
DU
Drugs
Consequent
X16
ST
Stress
Combination
X17
fsb
Feeling state for b
Dream
X18
srsST
Sensory representation state for ST
Dream
X19
csST,b
Control state for regulation of sensory represen-
tation of ST and feeling b
Dream
X20
desST
Dream episode state for ST
Dream
X21
Wsrs,cs
Reification state for connection weight srsST,csST,b
Dream
X22
Wfs,cs
Reification state for connection weight fsb,csST,b
Dream
• Protective: Protective states are states that protect a person against a clinical burnout; if they
have high values, then the chance of developing a burnout is lower.
• Risk: Risk states are states that increase the chance of developing a burnout.
• Burnout element: Burnout elements are affected by the protective factors and the risk factors,
they are the states that will grow in value when a burnout is developing. Looking at these
states is the best way to identify the level of burnout progression.
• Consequent: Consequent states are states that are affected by the burnout elements. By intro-
ducing a feedback loop from protective or risk states to burnout elements and then from burn-
out elements to the protective or risk factors, realistic positive or negative feedback becomes
possible. Thus, some states may have a consequent type, as well as another type.
• Dream: The dream type states are newly introduced in this model compared to previous lit-
erature on burnout modeling. These dream states regulate the emotions in an adaptive manner
as new dream episodes occur, as described in Section 2.
There are two special states shown in Table 4, namely state X21 and X22. These are the
reification states that introduce the adaptivity in the dream component of the model, as
described in [7]. These states use a Hebbian combination function, whereas the other
states all use a logistic function. Furthermore, state X16 has a type ‘combination’, which
was not mentioned above. According to [1], the main symptom of a clinical burnout is
the high stress level. Stress is an abstract concept that can be approached using multiple
emotions mentioned in Section 2. The stress state was added to the model as a state that
represents an overall effect some other important states in the model. The stress state is
not directly regulated; instead states X17 and X18 corresponding to the feeling state of
stress and the sensory representation of stress are regulated by the Control state X19. A
conceptual representation of the introduced adaptive network model is shown in Fig. 2.

6
This Fig. 2 shows two planes, of which the second plane (blue) represents the adapta-
tion states in the network: state X21 and X22 represent the values for the weights of the
connections from state X17 to state X19 and from state X18 to state X19, which allows the
connection weight values to change over time. In contrast to the simplified representa-
tion shown in Fig. 2, the actual model contains many more causal relations between all
states, as most emotions slightly affect each other, as shown in literature and mentioned
in Section 2. The network characteristics for connectivity (the connections and their
weights), aggregation (the combination functions and their parameters), and timing (the
speed factors) have been specified in the form of role matrices, which provides a com-
pact specification format for (adaptive) temporal-causal network models. For two of
them, mb and mcw specifying the connectivity characteristics, see Box 1.
Fig. 2. A simplified conceptual representation of the designed first-order adaptive temporal-
causal network. The upper plane indicates the adaptiveness of the model
Most of the values for these network characteristics were selected based on empirical
data as well as previous works like [4] and [5]. Role matrices have rows for all the states
and at each row indicate the elements that for the specific role have impact on that state.
For example, in Box 1 in mb it is indicated which other states have basic impact, and
in mcw it is indicated what is the connection weight impact for that state. Note that the
cells with nonadaptive values are green and the cells with adaptive values are red. In
the latter cells, not a value but the name of the reification state is specified which rep-
resents the adaptive value. This can be seen in the row for the control state X19, where
X21 and X22 are indicated as the states representing the adaptive values. Similarly, in
Box 2 a role matrix ms specifies what speed factor value has impact on the state, role
matrix mcfw specifies what combination function weights have impact and mcfp what
parameter values of the combination function. As can be seen in these role matrices, no
further adaptive characteristics were considered.

7
Box 1 Role matrices for the connectivity characteristics: role matrix mb (base connectivity)
and role matrix mcw (connection weights)
mb
1
2
3
4
5
6
7
8
9
10
11
12
State Abbr
X1
CO
PE
PA
JA
JS
NE
JP
JD
X2
OP
CO
PE
JS
NE
SC
JD
X3
PE
OP
X4
PA
CO
PA
CW
JA
JS
NE
EE
JP
JD
X5
NR
PE
PA
CW
JS
NE
EE
DU
X6
CW
CO
PE
PA
NR
CW
JA
JS
NE
SC
EE
JD
DU
X7
JA
CO
PA
NR
JA
JS
NE
SC
EE
JD
DU
X8
JS
PA
CW
JA
NE
EE
CY
JP
JD
X9
NE
CO
OP
PE
PA
NR
CW
JA
JS
SC
EE
JP
JD
X10
SC
CO
OP
PE
NR
NE
X11
EE
CO
OP
NR
CW
JA
JS
NE
JP
JD
DU
X12
CY
CO
OP
NE
EE
JD
X13
JP
CO
PA
NR
CW
JA
JS
NE
SC
EE
JD
DU
X14
JD
CO
PA
CW
JA
JS
NE
EE
CY
JP
DU
X15
DU
OP
PE
CW
NE
SC
EE
DU
X16
ST
EE
CY
JP
JD
X17
fsb
ST
csst,b
X18
srsST
ST
csst,b
X19
csST,b
fsb
srsst
desst
X20
desST
srsst
csst,b
X21
Wsrs,cs
srsst
csst,b
Wsrs,cs
X22
Wfs,cs
fsb
csst,b
Wfs,cs
mcw
1
2
3
4
5
6
7
8
9
10
11
12
State Abbr
X1
CO
0.5
1
-1
1
-1
1
-0.5
X2
OP
1
0.5
1
-1
1
-0.5
X3
PE
1
X4
PA
1
1
-0.5
-1
1
-1
-0.5
1
-1
X5
NR
0.5
0.25
-1
1
-0.5
-0.5
1
X6
CW
-1
-0.5
-0.5
-1
0.5
1
-1
1
-0.5
1
-1
1
X7
JA
-1
-1
-1
1
-1
1
-0.5
1
-1
-1
X8
JS
1
-1
-1
-1
-1
-0.5
1
-1
X9
NE
-0.25
-0.25
-0.25
-0.5
-0.5
1
1
-0.5
-0.5
1
-0.5
1
X10
SC
1
1
0.5
0.5
-1
X11
EE
-0.5
-1
-1
1
1
-1
1
-0.25
-1
-0.5
X12
CY
0.25
-1
0.5
0.25
1
X13
JP
1
1
1
-0.5
-0.75
1
-1
0.25
-0.5
-1
-1
X14
JD
-0.5
-1
-1
1
-1
1
1
1
-0.5
0.25
X15
DU
0.25
-0.5
0.25
1
0.25
0.25
0.5
X16
ST
1
1
-1
1
X17
fsb
1
-1
X18
srsST
0.5
-1
X19
csST,b
X22
X21
0.3
X20
desST
1
-1
X21
Wsrs,cs
1
1
1
X22
Wfs,cs
1
1
1

8
Box 2 Role matrices for the aggregation characteristics: role matrix mcfw (combination func-
tion weights) and role matrix mcfp (combination function parameter values); and role matrix
for the timing characteristics: role matrix ms (speed factors)
5 Simulation Results
This section shows the results obtained by running the model described in Section 4.
The model was simulated using the modeling environment described in [14] and [8],
Ch 9, using different initial values to create different scenarios. This modeling environ-
ment uses the above role matrices and initial values (and the step size t and end time
of the simulation) as input and then runs the simulations. These scenarios were tested
to gain a better understanding of the model and of clinical burnout progression. The
main scenarios tested are non-burnout versus burnout scenarios, which are obtained by
proper setting of the initial values of the relevant protective and risk states. Due to the
many causal relationships, initial values can severely impact the outcome of the simu-
lation. The scenarios were obtained by using the initial values for the states shown in
Table 5 and t = 0.01. Fig. 3 shows the progression of the states for a non-burnout
scenario (left) and a burnout scenario (right). For the non-bunout scenario the initial
values of the states that form high risks are low and the protective factors are high, as
can be seen in Table 5.
mcfp
hebb
alogistic
State Abbr
1

2
1

2

X1
CO
50
0.5
X2
OP
50
0.5
X3
PE
50
0.5
X4
PA
50
0.5
X5
NR
50
0.5
X6
CW
50
0.5
X7
JA
50
0.5
X8
JS
50
0.5
X9
NE
50
0.5
X10
SC
50
0.5
X11
EE
50
0.5
X12
CY
50
0.5
X13
JP
50
0.5
X14
JD
50
0.5
X15
DU
50
0.5
X16
ST
50
0.5
X17
fsb
50
0.5
X18
srsST
50
0.1
X19
csST,b
50
0.5
X20
desST
60
0.25
X21
Wsrs,cs
0.99
X22
Wfs,cs
0.99
mcfw
hebb
alo-
gistic
State Abbr
X1
CO
1
X2
OP
1
X3
PE
1
X4
PA
1
X5
NR
1
X6
CW
1
X7
JA
1
X8
JS
1
X9
NE
1
X10
SC
1
X11
EE
1
X12
CY
1
X13
JP
1
X14
JD
1
X15
DU
1
X16
ST
1
X17
fsb
1
X18
srsST
1
X19
csST,b
1
X20
desST
1
X21
Wsrs,cs
1
X22
Wfs,cs
1
ms
1
State Abbr
X1
CO
0.1
X2
OP
0.1
X3
PE
0.1
X4
PA
0.1
X5
NR
0.1
X6
CW
0.1
X7
JA
0.1
X8
JS
0.1
X9
NE
0.1
X10
SC
0.1
X11
EE
0.1
X12
CY
0.1
X13
JP
0.1
X14
JD
0.1
X15
DU
0.1
X16
ST
0.1
X17
fsb
0.1
X18
srsST
0.1
X19
csST,b
0.1
X20
desST
0.1
X21
Wsrs,cs
1
X22
Wfs,cs
1

9
Table 5. The initial values used for the non-burnout and burnout scenarios
State
X1
X2
X3
X4
X5
X6
X7
X8
X9
X10
Non-burnout
0.85
0.80
0.70
0.75
0.72
0.21
0.15
0.75
0.10
0.82
Burnout
0.25
0.22
0.23
0.20
0.35
0.90
0.95
0.30
0.98
0.17
State
X12
X13
X14
X15
X16
X17
X18
X19
X20
X21
Non-burnout
0.20
0.78
0.15
0.22
0.00
0.00
0.00
0.00
0.00
0.00
Burnout
0.15
0.90
0.05
0.075
0.00
0.00
0.00
0.00
0.00
0.50
The lines in the figure are colored based on their type: protective factors in green,
risk factors yellow, burnout elements red, consequences blue, dream factors magenta,
and finally, the stress state in black. The difference between states that share the same
type is shown using different line styles. The pattern can be explained by looking at
where the states are converging to. The protective factors are converging to one (all had
high initial values), while the risk factors converge to zero and (they had low initial
values).
Fig. 3. Non-burnout scenario (left) and a burnout scenario (right) simulated, all states except the
dream states are shown. States are colored by their type and can be distinguished by looking at
their line types.
When the initial values are changed to the values noted in the burnout scenario rows
in Table 5, the plot shown in the right hand side of Fig. 3 is acquired. This graph is a
bit more complex compared to the left graph, as more dynamics are shown. The figure
shows how the protective states, which have low initial values, converge to zero this
time. In contrast, the risk states, with high initial values, converge to one. This has
multiple repercussions for the model, as can be seen from the burnout element states
(red), EE and CY. As the burnout element states start to increase in value, the conse-
quent states (blue) are affected. For example, the job performance state, which had an
initial value of 0.90, starts to converge to zero, even though it had a high initial value.
Next to this, the consequent states job detachment and drugs, start to converge to one,
which starts to indicate the condition of the simulated person. Finally, the black line
shows the stress factor, which is a combination of the most important stress-related
states. At first, the stress level is not changing, until a tipping point is reached where it

10
starts to converge to one, as the consequent states are starting to affect the stress level
too much compared to the protective factors.
Fig. 4 shows the progression of the dream states during the burnout scenario simu-
lation. The dream states are not shown in Fig. 3 to prevent the figure from becoming
unreadable. The brown and purple lines in Fig. 4 indicate the reification states that show
the progression of the adaptive weights from the sensory representation state of stress
to the control state and the feeling state to the control state. The reification states are
affected by the control state, their own state, and respectively the sensory representation
state and feeling state. This can also be seen in Fig. 4, as the reification state Wsrs,cs
starts to increase when the control state as well as the sensory representation are in-
creasing and then starts to slowly decrease when the sensory representation state con-
verges to zero. The reification states increase due to the fear extinction learning cycle
[7], which means that when the connections are used more, they are strengthened over
time. Furthermore, the sensory representation state starts to increase rapidly, but when
the control state starts to increase, the sensory representation state starts to decrease,
until it converges all the way to zero. This is due to the negative emotion regulation
cycle, where the control state affects the feeling state and sensory representation state
as well as the dream episode state [7]. Dream episodes are generated by the sensory
representation state, which affects the control state as well. This simulation includes
one dream episode, which can be seen from the red line, that peaks around t = 20 and
then converges to zero. The interesting part of the figure, is where in contrast to the
sensory representation of stress, the feeling state starts to increase and then decrease,
which is in line with literature and the expected behavior, but then starts to increase
again due to the resonance with the control state. At that point, both the control state
and the feeling state of stress are resonating with one another and are creating a cycle
where they are both enforcing the behavior of each other. This continues until the feel-
ing state fsb reaches a point where its value is higher than the value of the control state,
after this they converge to their respective values.
Fig. 4. A display of the change in the dream states values during the burnout scenario simulation.

11
6 Empirical Validation
Although no numerical empirical data is available that outlines the exact influence that
emotions have on one another in a quantified manner, certain patterns can still be found
in the literature, which can be used to validate the model in an empirical manner. This
section will describe how the network model’s characteristics were tuned in accordance
with the patterns found in literature. In [4] and [5], the models were tuned in accordance
with respectively physical exercise and sleep components, which allowed for a more
realistic selection of parameter values.
This paper tunes the most import dream states, the feeling state and the control state,
in accordance with the patterns found in [7, 15, 16, 17]. This was done by first creating
data points in a manner that correspond with the noted literature. The data points used
can be found in Table 6. The pattern that would be acquired by tuning the parameters
to be in accordance with the data points, would be more in line with the emotion regu-
lation cycle, instead of the resonance pattern that was shown in Fig. 4. The network
characteristics that were selected to be tuned as parameters were the connection weights
for the incoming connections to the feeling state X17 and the control state X19, making
5 parameters in total.
To tune the parameters, a simulated annealing algorithm was used with the default
settings of Matlab’s Optimization Toolkit. A final Root Mean Squared Error (RMSE)
of 9.87*10-2 was acquired using 104 iterations. Table 7 shows the optimal values that
were found to achieve the RMSE in accordance with Table 6. After simulating the
model, using the initial values for the burnout scenario shown in Table 5, it can be seen
that the results are more in accordance with literature, as shown in Fig. 5. Extinction
learning and the reduction in feeling level can now be properly shown in accordance
with [5]. The resonance is still present, but in contrast to Fig. 4, the feeling state does
not surpass the control state, as they both converge before intersecting a second time.
Appendix B shows the development of the RMSE for every iteration during the tuning
process.
Fig. 6. Burnout scenario simulation using the optimal parameters found in Table 7 with the initial
values shown in Table 5 compared to the empirical data as dots.

12
Table 6. Data points created for the feeling state and control state in accordance with patterns
found in literature
Time
FSb
CSST,b
30
0.50
0.30
60
0.45
0.28
80
0.40
0.31
99
0.38
0.30
Table 7. Optimal parameter values found for network characteristics ST,fsb, csSTb,fsb and
desst,csSTb (indicated as parameters P1, P2, and P3, resp.) using simulated annealing to mini-
mize the RMSE in accordance with the points in Table 6.
ST,fsb
csSTb,fsb
desst,csSTb
P1
P2
P3
0.632
-0.333
-0.037
7 Mathematical Verification
The methods to verify if a model is mathematically correct described in [7] and [8]
were followed by checking some of the stationary points for the states. Stationary points
can be identified when dY(t)/dt = 0. Given the formulae in Section 3, a criterion for
finding a stationary point, is whether aggimpactY(t) = Y(t) holds, or cY(X1,YX1(t), …,
Xk,YXk(t)) = Y(t). This criterion can thus be used to identify stationary points in a tem-
poral-causal network. This was done for the burnout scenario described in Section 5.
The model was run until t=100 and then state fsb and state srsST were analysed to see
if they reached stationary points, by plotting the gradient of the states and finding the
points where the gradient is 0. The result can be seen in Fig. 6, which yields some of
the points that have been noted in Table 8 for analysis usable for mathematical verifi-
cation. To estimate the correctness of the model, four points for two states were ana-
lysed; the average error for the points as shown in Table 8 is 2.855*10-4, which is a
small error and is an indication of evidence that the model is mathematically accurate.
The errors were acquired by calculating the difference between the state values Xi(t)
and aggimpactXi(t), which is based on the logistic combination function with as input
the incoming state values with their corresponding weights, with  = 50 and  = 0.5 for
state X17 and  = 0.1 for state X18.
Table 8. Stationary point identification to verify the model
State Xi
X17
X17
X18
X18
Time point t
17.94
31.19
18.14
32.73
Xi(t)
0.4449
0.1303
0.6643
0.1665
aggimpactXi(t)
0.4446
0.1305
0.6648
0.1665
deviation
3*10-4
2.5*10-4
5.1*10-4
8.2*10-5

13
Fig. 6. Plot of the gradient of states fsb and srsst to identify where intersections are with y = 0,
which indicates stationary points
8 Discussion
The goal of this study was to design an adaptive temporal-causal network model incor-
porating dream components to create adaptive and more realistic burnout dynamics
than in earlier models [4, 5]. Not only dream states were added, the model was also
turned into a first-order adaptive model using a hebbian learning approach for adaptive
weights between states involved in dreaming. Using the methodology described in [7,
8] and the environment described in [14], a model was created that can be simulated as
well optimised. The results acquired by introducing dream states, do substantially differ
from previous work that only introduced states corresponding to sleep [5], as dreams
are powerful regulators of emotions such as fear [17].
Further application of the model may address a portrayal of how a clinical burnout
might develop, as this might give more insights into how they can be prevented. This
could be done for example, by creating an agent-based model, that keeps track of the
emotional wellbeing of a person and then scheduling them in manners where they gain
enough sleep which allows for enough dreams to take place, to prevent them from de-
veloping burnouts. One issue is still that there is no numerical data available, which
means that the model had to be validated based on qualitative empiric information using
a simulated annealing algorithm to tune parameters to find the behavior of the model
that is in accordance with the literature.
This paper serves as a first step to create an adaptive temporal-causal network de-
scribing burnout dynamics, which can still be expanded in the future, by adding more
real-life states. If more empirical data becomes available in regard to burnout, it will
also become possible to optimise the relationships between states, that were now based
on qualitative literature. When these components are optimised, a foundation can be
created to prevent, treat, or identify burnouts as well as gain a better understanding of
the underlying dynamics.

14
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