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An Adaptive Network Model for the Changes in Human Behaviour in Response to the Spread of COVID-19

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For a video presentation, see https://youtube.com/video/iimbJDkhEUc. The aim of the study reported here was to develop a model that can simulate the changes in human behaviour in response to the COVID-19 outbreak. To achieve this, a second-order adaptive social network model was designed integrating mental network models for each person. The model is based on adaptation principles such as the first-order Hebbian learning adaptation principle and the second-order 'adaptation accelerates with increasing exposure' adaptation principle.
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An Adaptive Network Model for the Changes in Human
Behaviour in Response to the Spread of COVID-19
Sharmayne Soh1, Shihan Yu2, Jan Treur3
1 Singapore Management University
2University of Amsterdam
3Vrije Universiteit Amsterdam, Department of Computer Science, Social AI Group
hzyushihan@gmail.com j.treur@vu.nl
Abstract The aim of the study reported here was to develop a model that can simulate
the changes in human behaviour in response to the COVID-19 outbreak. To achieve
this, a second-order adaptive social network model was designed integrating mental
network models for each person. The model is based on adaptation principles such as
the first-order Hebbian learning adaptation principle and the second-order adaptation
accelerates with increasing exposure adaptation principle.
1 Introduction
The Coronavirus Disease 2019 (COVID-19) pandemic has caused widespread effects on the
entire world. According to WHO, there have been over 194 million people confirmed of
COVID-19, and over 4 million deaths as of today [11]. With the spread of the virus, we have
seen significant changes to almost every aspect of our lives, including to our work, health,
and even day-to-day routines. The virus is believed to be transmitted mainly by close contact,
especially in indoor environments which have a higher risk of inadequate ventilation and
higher rates of close contact [3]. As a result, we have seen various measures taken to control
the spread of the virus, such as social distancing and mask-wearing.
Human behaviour plays a crucial role in preventing the spread of the virus. It is found that
other than pharmaceutical interventions, changing human behaviour is essential to curb the
transmission of the virus SARS-Cov-2 that causes COVID-19 [10]. In fact, behaviours such
as social distancing, mask-wearing and staying at home are key contributors to slowing down
the spread of the virus.
This paper focuses on building an adaptive network model to simulate the changes in be-
haviour of individuals in response to the spread of COVID-19. More specifically, this study
explores the changes in their behaviour based on their perceptions of the external state and
their own internal processes. With the aid of the model, we aim to have a better understanding
of how our internal processes can affect our response to external stimuli in the COVID-19
context.
2 Background Literature
To model the behavioural changes in response to the COVID-19 outbreak, we have looked
at existing literature related to this topic. Firstly, it is found that the COVID-19 virus is most
commonly transmitted by close contact, particularly in indoor environments as they are more
likely to have inadequate ventilation and higher rates of close contact amongst people [3], as
described by WHO. With this in mind, the next step would be to find out the preventive
methods to help curb the spread of the virus. It is found that the most essential and critical
ways to prevent transmission of the virus, excluding non-pharmaceutical methods, are in fact
largely related to human behaviour. Examples of such behaviours include social distancing,
the use of face masks, hand-washing and frequent disinfecting [10]. In fact, we found that it
was not just a one-way relation; not only does behavioural change impact the infection levels,
the spread of COVID-19 in turn also causes human behaviour to change. To support this, a
study conducted on the changes in human behaviour during the COVID-19 outbreak in Hong
Kong shows that human behaviour is significantly affected by the pandemic, where a 52.0%
fall was seen in the number of traveling passengers and 32.2% more time was spent at home
[12].
Through further research, other relevant literature found was a deep-learning study con-
ducted in the U.S. on human mobility and social behaviour in the COVID-19 context. This
study used a long short-term memory neural network (LSTM) to model the effective repro-
duction number of the COVID-19 spread, in order to capture its temporal dependence on
mobility and social behavioural variables. This LSTM explains the time lag between the
change in mobility and social behaviour, as well as its effect on the COVID-19 spread. In
addition, a sensitivity analysis showed that among the mobility parameters, being in enclosed
areas had the largest effect on the effective reproduction numbers, unlike open areas or transit
sites. In addition, all social behaviour parameters had relatively significant sensitivities, high-
lighting the importance of social interactions for the spread of the virus [2]. This supports the
fact that human behaviour, in particular concerning social interactions, indeed have an impact
on the spread of the COVID-19 virus.
3 The Self-Modeling Network Modeling Approach Used
The network-oriented modeling approach [9] applied, uses nodes (also called states) with
activation levels that vary over time and as network structure characteristics connection
weights for connectivity, combination functions c for aggregation and speed factors for
timing to specify a network model:
Connection weights: ωX,Y denotes the weight of the connection from node or state X to
State Y, and it usually ranges from -1 to 1.
Combination Functions: cX(..) denotes a combination function used for state X. From the
available library of combination functions, the following functions will be used in the intro-
duced model: alogistic,, hebb, stepmod,; see Table 1.
Speed factors: X with values usually between 0 and 1 denotes the speed of change of
state X with respect to the impact from other states.
Using the notion of self-modeling network (also called reified network) introduced in
(Treur, 2020), every network characteristic can be made adaptive by adding a (self-model)
state to the network that represents the value of this characteristic. This will be applied here
to obtain a second-order adaptive network in which for some states X and Y: (1) first-order
self-model states WX,Y are included in the network that represent the value of connection
weight X,Y, and (2) second-order self-model states HWX,Y are included in the network that
represent the value of the speed factor of WX,Y (learning rate).
Using the available dedicated software environment simulation is based on the following
equations based on the above network characteristics (where X1, …, Xk are the states from
which state Y gets incoming connections):
impactX,Y(t) = X,Y X(t) (1)
aggimpactY(t) = cY(impactX1,Y(t),…, impactXk,Y(t)) = cY(X1,YX1(t), …, Xk,YXk(t)) (2)
Y(t+t) = Y(t) + Y [aggimpactY(t) - Y(t)] t
= Y(t) + Y [cY(X1,YX1(t), …, Xk,YXk(t)) - Y(t)] t (3)
Table 1 The combination functions used in the introduced network model
Notation
Formula
Parameters
Steponce
stepmod(V)
0 if t mod , else 1
repetition interval length, step time
Advanced
logistic
sum
alogistic,(V1, …,Vk)
󰇟
󰇛
󰇜

󰇜󰇠(1+e-στ)
Steepness > 0
Excitability threshold
Hebbian
learning
hebb(V1, V1, W)
V1V2 (1-W) + W
V1,V2 activation levels of the connected
states; W activation level of the self-
model state for the connection weight
persistence factor
4 The Adaptive Network Model
According to the study by Gentili and Cristea (2020) [4], the most widely explored preventive
methods for COVID-19 are non-pharmaceutical therapies. These include maintaining a social
distance, mask-wearing, hand-washing, and frequent disinfecting. For our the scenarios ad-
dressed by our model, we have identified three of these behaviours that different individuals
could exhibit, in order to study the different adaptations of their responses to the COVID-19
infection levels. The designed model provides a second-order adaptive network architecture
to simulate behavioural adaptation of humans in the COVID-19 context. It covers both the
social network of connections between persons and these persons internal mental processes.
4.1 The social network model
Based on data extracted from Hung et. al (2020) [6], we have selected three commonly ex-
hibited behaviours in society to be used in our simulation scenario: whether an individual (i)
keeps a 1.5 meter distance from others, (ii) wears a mask, and/or (iii) stays at home. Table 5
(see the Appendix section) shows the different possible combinations in which eight hypo-
thetical individuals could exhibit (some of) the aforementioned behaviours. The extent to
which people exhibit risky behaviour will not only have an impact (through social contagion)
on the behaviour of other individuals, but also on the infection levels, and vice versa. Fig. 1
shows the connections between the eight individuals.
Fig. 1: The example social network addressed
We separated these individuals into two distinct social groups and Fig. 1 also shows links
between these groups. For instance, Person A stays at home, wears a mask and observes a
social distance of 1.5m, which makes him/her unlikely to come into contact with Person H
who fails to take any precautions. Since staying at home is the most efficient way to prevent
contact between people, we therefore categorised Persons A to D in one social group and the
rest in another social group. The possible interactions between Groups 1 and 2 include B with
F and B with G, as they are the people that do not stay at home. These are hence the two most
likely sites of contact between the two social communities.
4.2 The Adaptive Mental Network Model
In order to simulate both the behaviour and the underlying learning of the individuals, our
model also exploits the concept of network adaptation. For this, a second-order adaptive net-
work architecture is used; the overall multi-level adaptive network model is expressed graph-
ically in Fig. 2 (see Fig. 3 for a more detailed picture of the mental network model of a
person).
Fig. 2: The overall second-order adaptive network model
In this figure, the pink plane denotes the base level, while the blue and purple plane represent
the first-order and second-order adaptation levels, respectively. Therefore, the generic archi-
tecture of the multi-level adaptation process consists of three main levels: the base level, first-
order adaptation and second-order adaptation [9]. The base level describes the dynamics
within the network, which we have established earlier in the Social Network Model. The
first-order adaptation represents the adaptation of the network itself by certain adaptation
principles, which in this case concerns changes in behaviours of the individuals based on the
behaviour learning. In Fig. 2, the first-order adaption level models Hebbian learning [5] and
is represented by the blue plane. The second-order adaptation is the adaptation of these ad-
aptation principles [1], which is reflected by the speed of change in the adaptation of such
behaviours in our model; this is based on the second-order ‘adaptation accelerates with ex-
posure adaptation principle formulated in [8].
In Table 2 an overview of the different states can be found with their explanation. In Tables
3 and 4, an overview is provided of all types of connections used and their effects. Note that
for the sake of transparency, not all connections are included in Fig. 2.
Table 1 Description of the states
State
Description
wsi
World state for the infection level
srsi,X
Sensory representation state of Person X for the infection level i
srsc,X
Sensory representation state of Person X for the general context c
psX
Preparation state of the behaviour of Person X
srse,X
Sensory representation state of Person X for the (predicted) effect e of the prepared
behaviour
esX
Executing state of the behaviour of Person X; note that a low value means that the
person behaves in a safe manner by taking into account measures against infection and
a high value means that the person does not take such measures into account.
sroX
Sensory representation state of Person X for other people’s behavior
Wsrsc,X,psX
First-order self-model state for the weight of the connection from srsc,X to psX
Wsrse,X,psX
First-order self-model state for the weight of the connection from srse,X to psX
HWsrsc,X,psX
Second-order self-model state for the speed factor of the first-order self-model state
Wsrsc,X,psX
HWsrse,X,psX
Second-order self-model state for speed factor of the first-order self-model state
Wsrse,X,psX
Table 2 Description of the types of connections used at the base level
Connection type
Intra-person links
srsc,X psX
srsi,X psX
psX esX
psX srse,X
srse,X psX
sroX psX
Extra-person links
esY sroX
wsi srsi,X
esX wsi
Base level processes
The base level interactions are graphically represented in the lower plane in Fig. 2; see also
Table 2. Generally, since the world state wsi represents information on the general infection
level of the population, this information affects each person’s sensory representation state
srsi,X for the infection level. In turn, the world state wsi will also be affected by the execution
states esX for the behaviour of our individuals A to H. As higher values of these states indicate
bad behaviour, such higher values have an increasing effect on the general infection level
wsi. Besides the world state for the infection level, other external stimuli that will influence
the internal processes of each individual X concern the behaviours esY of the other individuals
Y in the social network. This happens in each subgroup separately, but for interactions be-
tween the social groups, Person B from Group 1 has contact with Person F and G from Group
2. In our model, an example of a connection weight is ωwsi,srsi,A , which represents the weight
of the connection from the world state wsi (infection level) to the sensory representation state
srsi,A for the infection level perceived and represented by Person A. Another example is
ωsrsi,X,psX, the weight for the connection from srsi,X to psX. As the connection from this sensory
representation state for infection level to the preparation state of each person is assumed to
be suppressing, the connection weights ωsrsi,X,psX will be negative. In the model, we used -0.5
to represent this negative weight. Since each of the individuals’ behaviours are risky to dif-
ferent extents, they would have varying impacts on the overall infection level. As such, we
allocated different (initial) connection weights ranging from 0.4 to 0.9 to each individual,
with staying at home having the highest weight, followed by wearing a mask, and lastly
keeping a 1.5m distance having the lowest weight. Additionally, as the connection between
Social Group 1 and Group 2 is relatively weak, we assigned those with values ranging from
0.4 to 0.5.
The advanced logistic function, alogistic,(..), is used for all base level states with the
exception of the sensory representation state srsc,X for the general context for each person.
The srsc,X states will instead apply the stepmod function to model a repetitive type of context.
All sixteen W-states use the Hebbian combination function denoted by hebb(..), that models
the first-order adaptation principle for Hebbian learning. The sixteen H-states also apply the
combination function alogistic,(..).
Fig. 3: The internal mental network model of Person A
To explain the internal mental network model of each individual in further detail, a picto-
rial representation of an individual’s internal mental model can be found in Fig. 3, taking
Person A as an example. We first start by looking at the overall infection level wsi and the
general context. As the individual perceives such external stimuli, his/her sensory represen-
tation states srsi,X and srsc,X for the infection level and the general context will be activated.
Moreover, also the behaviours of other persons that are connected lead to an aggregated rep-
resentation state sroX of these behaviours. Following all these, the person’s sensory represen-
tation states srsi,X, srsc,X, sroX for the infection levels, general context, and other people’s be-
haviour collectively affect his/her preparation state psX. Here the connection from sroX to psX
models in particular a mirroring link; e.g., [7]. Moreover, another contribution to the activa-
tion of the preparation state psX comes from the predicted effect representation state srse,X,
which is activated through a prediction link from psX to srse,X which creates a prediction loop
between the preparation state psX and the sensory representation srse,X for effect e. Eventually,
the person’s preparation to make a decision on his/her behaviour will lead to the executing
state esX. The execution of each person’s behaviour would not only influence the sensory
representation state sroX of other individuals in their social group, but also influence the over-
all infection level wsi. In accordance with what is listed in Table 2, for the considered example
Mirroring link
network extra-person connections exist from esB to sroG, esB to sroF, esF to sroB, and esG to
sroB.
Table 3 Description of the types of connections used for the self-model states
Connection type
Connections for the first-order self-model states
srsc,X Wsrsc,X,psX
psX Wsrsc,X,psX
Wsrsc,X,psX Wsrsc,X,psX
srse,X Wsrse,X,psX
psX Wsrse,X,psX
Wsrse,X,psX Wsrse,X,psX
Wsrsc,X,psX psX
Wsrse,X,psX psX
Connections for the second-order self-model states
srsc,X HWsrsc,X,psX
psX HWsrsc,X,psX
Wsrsc,X,psX HWsrsc,X,psX
srse,X HWsrse,X,psX
psX HWsrse,X,psX
Wsrse,X,psX HWsrse,X,psX
HWsrsc,X,psX Wsrsc,X,psX
HWsrse,X,psX Wsrse,X,psX
First-order adaptation
The first order adaptation processes, as represented within the middle (blue) plane in Fig. 2,
build on the base level by modelling the adaptation of the behaviours of the eight individuals.
These adaptations the place by the learning of the behaviours from the base level discussed
above. As shown in Fig. 2, there are two first-order self-model states (at the first reification
level) for each individual: Wsrsi,X,psX represents the weight for the connection from srsi,X to
psX, and Wsrse,X,psX represents weight of the connection from srse,X to psX. These weights are
(partly) based on learning by a form of social contagion realized by internally mirroring oth-
ers’ behaviours. They determine the changes in the sensory representation state and prepara-
tion state of each individual that are used to generate her/his behaviour.
Second-order adaptation
Next, the second-order adaptation, as represented within the upper (purple) plane in Figure
2, explains the adaptation (or control) of these adaptation principles, which is reflected by
the speed of the change of the individuals’ behaviours. Here, there are two (second-order)
self-model states for each person: HWsrsi,X,psX represents the speed factor for Wsrsi,X,psX and
HWsrse,X,psX represents the speed factor for Wsrse,X,psX. These adaptive speed factors model the
effect of (stimulus) exposure on the speed of change in the individuals’ behaviours according
to the second-order adaptation accelerates with increasing exposure adaptation principle.
5 Simulation Results
In this section, some of the simulation results are discussed. The example scenario is based
on the social network depicted in Fig. 1 and the more specific network models depicted in
Fig. 2 and Fig. 3. More details about the network characteristics used can be found in the
Appendix Section 7. The duration applied to our simulation is 800, and the interval iteration
Δt was set to 0.25. Since all mental states are not affected by any prior states, the initial values
for all mental states (i.e., srse,X, esX, psX, etc.) were set to 0. The initial values for the states
that use Hebbian learning (all W states) were set to 0.1, and the world state of infection level
was set to start with an initial value of 0.5.
Fig. 4: Comparison of Simulation Results for Social Group 1
Overall Results
As there was a total of 81 states, we categorised the states into each individual and generated
a separate graph with simulation results for each person for a better view. Figs. 4 and 5 dis-
play the results of the simulation for Person A to H. The curved blue line in the middle of
each figure represents the world state of infection, which is the general infection level. The
overall trend of the wsi state suggests that the infection rate will initially decrease. However,
as people learn more of the bad behaviour over time, the infection rate will begin to increase
again.
Fig. 5: Comparison of Simulation Results for Social Group 2
Results Social Group 1
Comparing the results in Fig. 4, Person A and Person C are less affected by the learning of
bad behaviour, whereas Person B and Person D start to behave poorly from the second and
first cycle respectively. The light blue line which represents the execution state esX fluctuates
considerably in the graphs for Persons A to C, but remains almost stable for Person D. While
those who are more compliant with the social distancing behaviours are more likely to be
cautious about the transmission of the virus, there could also be a tendency for their behaviour
to become poorer after learning of the bad behaviours.
Results Social Group 2
As for the second social group in Fig. 5, the starting time of their learning is later than those
in the first group. This could be attributed to the fact that since they already engage in two or
three bad behaviours, their learning will take place relatively later than those who initially
exhibit good social distancing behaviours. Despite this, even though the Group 2’s starting
time for learning is later, the sensory representation states srsi,X in Group 2 have a steeper
increasing trend compared to Group 1. This is represented by the dark red lines for each
person in Figs. 4 and 5, which suggest that people in Social Group 2 require less time to
respond to the information they receive from the external environment about the infection
levels.
Comparison of the Execution States
Fig. 6 shows a comparison of the execution states esX of each individual. Generally, the exe-
cution states of every person reach the same end-point eventually. For Person B and D, the
onset of their behavioural change are the earliest among the eight individuals, as represented
by the two purple lines. This means that not wearing a mask and staying at home influence
behavioural change more, subsequently.
Fig. 6: Comparison of Execution States
Comparison of the W-States
Fig. 7 depicts the comparison of the behavioural learning, as modelled by the W-states, for
Persons A to H in two different scenarios. In the first scenario, where the Hebbian learning
parameter (μ) was set to 1, Person B’s, D’s and H’s learning begin considerably early, while
Person E and F begin to learn relatively later.
Fig. 7: Comparison of Behavioural Learning (W-states)
Also, for Person A, B, C, D, F and G, their learning process for Wsrsc,X,psX and WsrseX,psX
yield fairly similar results, except for a slight difference where their learning process for
WsrscX,psX occurs more slowly than their prediction effect Wsrse, X,psX. On the other hand, for
Person E and H, the learning of WsrscE/H,psE/H and Wsrse,E/H,psE/H have a large difference in their
graphs. In this first scenario where the persistence parameter μ for Hebbian function was set
to 1, the learning for all individuals first increased and then stayed constant at 1 over time.
In the second scenario however, where the persistence factor μ was set to 0.95, although
the learning increased for almost all individuals initially, they eventually returned to their
original levels for those in Social Group 1 (Fig. 7(c)). One example would be Person A, as
represented by the yellow line, whose learning initially increases but soon after decreases to
its original level.
6 Conclusion and Discussion
The aim of this study was to develop a model that could simulate the changes in human
behaviour in response to the COVID-19 outbreak. To achieve this, we applied a social net-
work model with included internal mental network models, as well as adaptive principles
such as Hebbian learning to form a second-order adaptive network model. The results agree
to our initial expectations, and we have drawn three main findings from the results.
Firstly, individuals that exhibit any type of behaviour will eventually tend to start learning
bad behaviour. The results showed a tendency for the infection levels to increase over time.
Although those who take more precautions (such as those in Group 1) are more likely to be
cautious about the spread of the virus, their behaviour tend to become poorer as their learning
of the bad behaviours increase. As a result, more infections occur and the world state of
infection increases.
Secondly, different behaviours exhibited by individuals would have varying levels of in-
fection, and hence have differing impacts on learning. In particular, the results show that
those who do not wear masks generally have earlier starting points for their learning. In ad-
dition, those who do not wear masks and do not keep a 1.5 meter distance learn more slowly
than those who do not stay at home.
Furthermore, poor performers, i.e., those who initially engage in two or three bad behav-
iours, typically have a later starting learning point than those who observe social distancing
behaviours, such as those in Group 1. To add on, these poor performers who exhibit undesir-
able behaviours also learnt at almost the same rate, but those who started with more desirable
behaviours started learning earlier but more slowly than those who exhibit more undesirable
behaviours.
For the current version of the model, there are some areas that could use further consider-
ation. Firstly, the speed factor for the world state was set to 0.05, but there is still a fair bit of
uncertainty in the speed of transmission of the virus. Therefore, further research could be
conducted on the speed factor of wsi in the simulation. Furthermore, as this social network
model is a simplified version of reality, the current model could be improved to suit the com-
plexities of social interactions in the real world, such as including more types of behaviours.
7 Appendix: More Details
In this section some more details of the simulation scenario are discussed. For the full speci-
fication, see URL ** under Linked Data. Table 5 shows the assumed combinations of behav-
iours considered in the simulation scenario.
Table 5: Combinations of Behaviours for Individuals A-H
Person
Behaviour
A
Wears a mask, Keeps 1.5m distance, Stays home
B
Wears a mask, Keeps 1.5m distance, Does not stay home
C
Wears a mask, Stays at home, but does not keep 1.5m distance
D
Keeps 1.5m distance, Stays at home, but does not wear a mask
E
Stays at home, but does not wear a mask, and does not keep 1.5m distance
F
Keeps 1.5m distance, but does not wear mask, and does not stay at home
G
Wears a mask, but does not keep 1.5m distance and does not stay at home
H
Does not wear a mask, does not keep 1.5m distance, does not stay at home
The following table shows the values for the respective parameters for each state. Gener-
ally, 50 was used as the repeated time duration and was 20 for the states with the stepmod
function. For states applying the Hebbian function, the persistence factor μ was valued at 1.
As for the states applying the advanced logistic sum function, a steepness of 5 was used in
general, with the exception of a few states with different threshold values 0.5-2.
The speed factor represents the speed of the process to reach its corresponding state. For
instance, ηsrsi,X represents how fast Person X perceives and internalises the latest COVID-19-
related news. Since news is often received at varying speeds by different people with different
behaviours, their corresponding speed factors for their sensory representation states would
also have differing values. Speed factors of 0.1, 0.4, 0.7 and 1 were allocated to the eight
individuals who exhibit none to all three behaviours. Furthermore, because mental states will
always be constructed faster than actions, the preparation state psX would have a higher speed
factor of 0.8, while the executing state esX would have a slower speed of 0.3. The different
speed factors for each state are shown in the Table 6.
Table 6: Speed Factor for Each State
wsi
srsi,A
srsi,B-D
srsi,E-G
srsi,H
psX
esX
Others
0.05
0.1
0.4
0.7
1
0.8
0.3
0.5
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In this paper, we review experimental evidence for a novel form of persistent synaptic plasticity we call metaplasticity. Metaplasticity is induced by synaptic or cellular activity, but it is not necessarily expressed as a change in the efficacy of normal synaptic transmission. Instead, it is manifest as a change in the ability to induce subsequent synaptic plasticity, such as long-term potentiation or depression. Thus, metaplasticity is a higher-order form of synaptic plasticity. Metaplasticity might involve alterations in NMDA-receptor function in some cases, but there are many other candidate mechanisms. The induction of metaplasticity complicates the interpretation of many commonly studied aspects of synaptic plasticity, such as saturation and biochemical correlates.
Mirroring People: the New Science of How We Connect with Others
  • M Iacoboni
Iacoboni M. (2008). Mirroring People: the New Science of How We Connect with Others. New York: Farrar, Straus & Giroux (2008)