# Optimal prevention strategies for chronic diseases in a compartmental
disease trajectory model

Katharina Ledebur1,3,4 Alexandra Kautzky-Willer2 Stefan Thurner1,3,5 Peter
Klimek1,3,4∗

( 1Section for Science of Complex Systems, CeMSIIS, Medical University of
Vienna, Spitalgasse 23, A-1090 Vienna, Austria
2Gender Medicine Unit, Division of Endocrinology and Metabolism, Department of
Internal Medicine III, Medical University of Vienna, Spitalgasse 23, A-1090
Vienna, Austria
3Complexity Science Hub Vienna, Josefstädter Strasse 39, A-1080 Vienna,
Austria
4Supply Chain Intelligence Institute Austria, Josefstädter Strasse 39, A-1080
Vienna, Austria
5Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
<EMAIL_ADDRESS>
)

###### Abstract

In countries with growing elderly populations, multimorbidity poses a
significant healthcare challenge. The trajectories along which diseases
accumulate as patients age and how they can be targeted by prevention efforts
are still not fully understood. We propose a compartmental model,
traditionally used in infectious diseases, describing chronic disease
trajectories across 132 distinct multimorbidity patterns (compartments).
Leveraging a comprehensive dataset from approximately 45 million hospital
stays spanning 17 years in Austria, our compartmental disease trajectory model
(CDTM) forecasts changes in the incidence of 131 diagnostic groups and their
combinations until 2030, highlighting patterns involving hypertensive diseases
with cardiovascular diseases and metabolic disorders. We pinpoint specific
diagnoses with the greatest potential for preventive interventions to promote
healthy aging. According to our model, a reduction of new onsets by 5% of
hypertensive diseases (I10–I15) leads to a reduction in all-cause mortality
over a period of 15 years by 0.57 (0.06)% and for malignant neoplasms
(C00–C97) mortality is reduced by 0.57 (0.07)%. Furthermore, we use the model
to assess the long-term consequences of the Covid-19 pandemic on
hospitalizations, revealing earlier and more frequent hospitalizations across
multiple diagnoses. Our fully data-driven approach identifies leverage points
for proactive preparation by physicians and policymakers to reduce the overall
disease burden in the population, emphasizing a shift towards patient-centered
care.

##  1 Introduction

In many western countries, there is a persistent trend of increasing life
expectancy [1]. From 1999 to 2019, life expectancy in Europe increased by 7.8%
[2], and specifically, in Austria by 3.8% and 6.0% for women and men,
respectively [3]. This trend is expected to continue. By 2050, the proportion
of the Austrian population over 65 years will increase from 19.4% (2019) to
27.7% [4, 5]. However, since 2011, the rate of increase in life expectancy has
been slowing down in several EU countries, mainly due to a slowdown in
improvements in mortality from cardiovascular disease and potentially due to
increasing prevalence of diabetes and obesity [6]. In Austria, the life
expectancy in self-perceived (very) good health decreased from 65.9 (2014) to
63.1 years (2019) for men and from 66.6 (2014) to 64.7 years (2019) for women
[7, 8]. The increase in total life expectancy together with the decrease of
life expectancy under healthy conditions may be explained in part by excellent
acute medical care and emergency medicine, and at the same time, a lack of
adequate prevention programs for noncommunicable diseases (NCDs) which would
be necessary to improve health of an aging population [9].

An aging population is associated with an increase in the prevalence of
chronic diseases [10]. As chronic diseases often share risk factors, this is
expected to increase the number of people with multiple health conditions
[11]. This phenomenon, referred to as ’multimorbidity’, is one of the major
challenges facing countries with aging populations [12]. Most research on the
increase in multimorbidity focuses either on a small or a specific subset of
individuals [13, 14, 15] and/or specific chronic diseases [16, 17, 18].
Research on multimorbidity itself, in a broader context is rare, despite its
pressing development, and varies in terms of study setting, data sources,
study population and type of measure [19]. One reason for this knowledge gap
is the lack of a clear definition of multimorbidity [20]. Studies often define
multimorbidity as the presence of a certain number of diagnoses (two or more).
However, disease progression and treatment depend strongly on which diseases
co-occur [21, 12]. An alternative to simply defining multimorbidity by the
count of diagnoses would be to define multimorbidty as the presence of disease
patterns in the form of sequences of diseases individuals are diagnosed with
over their life-course, so-called disease trajectories [22].

The field of network medicine has advanced the understanding of the nature of
disease trajectories through numerous studies of so-called phenotypic
comorbidity networks, where nodes represent diseases and links describe their
associations, the observed relationships between diseases and various factors
such as genetics, lifestyle, or environmental exposures. Population-wide
electronic health records (EHR) or medical claims data have also allowed us to
identify such trajectories on a large scale [23, 21, 27, 28, 29, 30, 31, 32,
33, 24, 25, 26]. Specifically, it was found that patients tend to develop
diseases that are in close network proximity to diseases they have already
been diagnosed with. This facilitates predicting future diseases based on
medical history [23, 21]. A major challenge in studying long-term disease
trajectories is the large number of possible disease combinations and their
temporal permutations. By clustering frequently co-occurring diseases and
quantifying how they condition each other, it is possible to reliably uncover
long-term disease trajectories, as a series of disease combinations (health
states), for populations within countries [22, 34]. However, studies on the
temporal evolution of multimorbidity, especially in the context of an aging
population, remain scarce, both in terms of retrospective data analyses [35,
36, 37], and for predictive modelling. The bottlenecks are methodological
challenges and data requirements [38, 39].

Nevertheless, disease trajectory modelling holds the promise of identifying
leverage points for optimal prevention schemes derived from a quantitative
basis. Recent research suggests the existence of "critical points" or high-
risk points in disease trajectories [22]. These points represent combinations
of health conditions that, when taken together, inevitably increase the risk
of acquiring further diseases and, ultimately, mortality. Prevention schemes
should then be designed to target patient groups before they reach these
"points of no return". Predictive and fully interpretable models for how
patients follow their disease trajectories can then be used to perform ex ante
assessments of a large set of potential prevention strategies to identify
those that lead to optimal outcomes.

There is a tradition of using both quantitative network-based approaches and
compartmental frameworks, to describe the health status of individuals, to
study the public health effects of interventions, and to forecast
epidemiological developments in the context of infectious diseases. This
became apparent during the Covid-19 pandemic, where such models played a
pivotal role in decision support. While hitherto such modelling approaches
have remained largely unexplored for NCDs. Why there is such a remarkable
methodological gap between communicable and noncommunicable diseases is not
entirely clear. One reason may be that it is not clear to date if and how the
disease-causing mechanisms that underlie chronic diseases can be put into
mathematical language.

Here, we close this gap by developing a compartmental, network-based model for
the investigation of chronic disease trajectory dynamics within the Austrian
population. Our starting point is the observation that many chronic diseases
tend to co-occur due to a shared disease etiology. For instance, diagnoses
such as hypertension, dyslipidemia, or overweight (the metabolic syndrome) are
well known risk factors for type 2 diabetes [40]. Diabetic patients are
frequently diagnosed with diagnoses like polyneuropathy, stroke,
cardiovascular diseases, or combinations thereof [41]. We identify groups or
"multimorbidity clusters" of frequently co-occurring diagnoses (a cluster for
the metabolic syndrome, several clusters for diabetic complications, etc.) and
quantify how likely patients progress from one specific cluster to another
over time. The result is a compartmental model in which every patient is
assigned a health state, a cluster, per year. While for infectious disease
dynamics these compartments typically correspond to e.g. susceptible,
infected, or recovered individuals, for chronic diseases these compartments
correspond to different multimorbidity clusters.

The approach is outlined in Figure 1. Using an extensive dataset covering all
hospital diagnoses in Austria between 1997 and 2014 (approx. 45,000,000
hospital stays of about 9,000,000 individuals), a transition network between
multimorbidity clusters describing patterns of co-occurring diseases (ICD-10
codes covered range from A00 to N99) was developed by Haug et al. (2020) [22].
Here, we extend this framework to a population-dynamics compartmental model
and simulate the multimorbidity patterns of the entire Austrian population
from 2003 to 2030, incorporating demographic changes (migration, birth, and
death provided by the Austrian National Statistics Office) as well as
individuals acquiring new diagnoses on the basis of their multimorbidity
cluster, enabling both in- and out-of-sample predictions. Both, the incidences
of the different diagnoses and the temporal development of multimorbidity
within the population can be addressed in the new framework.

We demonstrate the versatility of this novel compartmental disease trajectory
model (CDTM) in several case studies. Initially, we forward project the annual
incidence of diagnoses (A00-N99) and combinations thereof in a baseline
scenario. This projection considers the predicted changes in demographics by
the national statistics office but no improvements in death rates, diagnostic
procedures, treatments, etc. Subsequently, we conduct a series of simulations
to assess the overall and long-term impact of hypothetical disease prevention
efforts. We focus on specific diseases and assume that new therapies or
increased surveillance lead to improved prevention rates for these diagnoses,
resulting in a reduction in new onset diagnoses. Our model enables us to
compute how this decrease in diagnoses affects the risk to progress to other
multimorbidity patterns and their associated mortality across the entire
diagnostic spectrum. By comparing the simulations of each hypothetically
prevented diagnosis, we can quantitatively estimate which kind of preventions
lead to the greatest overall reduction in mortality. Additionally, we study
scenarios for the long-term impact of the Covid-19 pandemic. We estimate the
impact of sequelae of a SARS-CoV-2 infection on the disease burden and
expected deaths in the Austrian population in a pessimistic and optimistic
scenario.

Figure 1: Workflow of the research presented in this article, construction of
multimorbidity network and compartmental disease trajectory model (CDTM). (a)
The diagnostic history of all patients (alive between 1/1/1997 and 12/31/2002)
is collected. According to these diagnoses, each patient is assigned to a
multimorbidity cluster as identified by Haug et al. (2020) [22]. The model is
initialized in a state that is calibrated to the Austrian population at the
beginning of 2003. We validate the model until 2014 and simulate the disease
trajectories of the Austrian population until 2030. (b) The multimorbidity
network was constructed by extracting patient histories from all hospital
stays between 2003 and 2014 consisting of diagnoses $d_{i}$ that they may or
may not have had (large and small circles, respectively) up to year $t_{j}$.
From this data matrix, 132 distinct multimorbidity clusters were identified by
means of a divisive clustering algorithm. These clusters are the network
nodes. Disease trajectories of the patients can then be described as patients
transition between multimorbidity clusters with age- and sex-specific rates
(network links in (c)). (c) In this compartmental model, individuals are
assigned a disease cluster each year based on their previous year’s cluster
and the corresponding age- and sex-stratified transition probabilities.
Additionally, the model incorporates annual processes of birth, migration, and
death.

##  2 Methods

###  2.1 Data Characteristics and Compartmental Disease Trajectory Model
(CDTM)

The compartmental, network-based approach employed in this study relies on a
comprehensive dataset provided by the Austrian Ministry of Health. The dataset
covers all hospital records from all hospitals in Austria from 1997 to 2014.
The dataset covers over 45 million stays for over 9 million different
individuals. For each stay, the sex, age-group (5-year interval), duration of
the stay, exit reason as well as main and side diagnoses on three digit level
ICD-10 codes are recorded.

To construct the multimorbidity network underlying the compartmental disease
trajectory model (CDTM), we follow a recently proposed machine learning
approach [22]. All diagnoses for a specific subset of individuals are
extracted from the dataset (individuals who did not receive a diagnosis from
1997-2002 but did receive a diagnosis from 2003-2014) and the health state per
patient and year are encoded as binary vectors, Figure 1b. Each entry
corresponds to one of the 131 diagnose groups defined by the WHO. An entry
with a value of 1 indicates that the individual was diagnosed with the
respective diagnosis group, while a value of 0 indicates the absence of such a
diagnosis. Note that these diagnoses are cumulative, indicating that an
individual remains diagnosed with a disease throughout the observation period,
as the dataset lacks information on the resolution or recovery of diagnoses
over time. A hierarchical clustering algorithm (DIVCLUS-T) identified 132
multimorbidity patterns. These patterns, multimorbidity clusters, serve as
nodes in a multiplex network, with directed edges representing transition
probabilities between these patterns. Each layer of the network corresponds to
a specific age and sex group. The directed edges between two clusters $k$ and
$j$ are weighted based on the age- ($a$) and sex ($g$) dependent probabilities
($q_{g,a,k,j}$) of transitioning from one cluster to another within a single
time step.

The nodes and links in this multilayer network provide the basis for the
states and their transitions in a compartmental model, see Figure 1c.

We model the Austrian population by extracting all diagnoses of individuals
with a hospital stay in the dataset from 1997-2003 and assigning them a
multimorbidity cluster (compartment or network node) following Haug et al.
(2020) [22]. We compare the number of individuals per age and sex group with
the actual population size according to Statistics Austria at the start of
2003 and add the difference as into a compartment of individuals with no
hospital stays at all (cluster 0). (Figure 1a) [4]. Individuals in the
population are modeled as random walkers transitioning over the multimorbidity
network. In particular, the model assumes that an individual with sex, $g$,
and age, $a$, assigned to cluster, $k$, transitions to another cluster $j$
with probability $q_{g,a,k,j}$, as observed in the data.

Each multimorbidity cluster is defined by a set of 131 probabilities $p_{c,d}$
describing the probability of being diagnosed with diagnose group $d$, given
that the patient is in cluster $c$. We calculate for each cluster and diagnose
group a probability of being diagnosed with the respective group when
transitioning to that cluster.

###  2.2 Calibration and Simulation

In each simulation year, individuals are assigned a specific multimorbidity
cluster based on age and sex-dependent transition probabilities $q_{g,a,k,j}$.
If an individual’s cluster assignment differs from that of the previous
simulation year, they are subsequently diagnosed with diseases in accordance
with the probabilities associated with the 131 diagnostic groups corresponding
to their new cluster ($p_{c,d}$). This dynamic process enables the model to
project and predict disease incidences on a yearly basis.
Also on an annual basis the model incorporates several demographic factors:
individuals are born, migrate, and pass away according to historical data and
a baseline scenario of population movements provided by Statistics Austria
[4]. The number of deaths per cause (i.e. a specific disease) are only
available until 2019. From 2019 onwards, our assumption is the distribution of
deaths by cause from 2019 onwards. Forecasts of deaths by age and sex from
2019 onwards are only available for scenarios that already include the effect
of the Covid-19 pandemic. Therefore, we use the 2019 projections and assume
the same sex and age distribution of deaths from 2019 onwards to establish a
baseline without the impact of the pandemic [42]. To calibrate the model, we
adjust the age and sex-dependent transition probabilities by applying an age-
dependent factor.We reduce the transition probabilities for the first three
ten-year age groups (0-29 years) by 65%, for the age group 30-39 years by 60%,
for the age group 40-49 years by 40%, for the age group 50-59 years by 20% and
for the age group 60-69 years by 10%. The transition probabilities of the last
three ten-year age groups (70+ years) are not reduced. The reduction factors
were estimated via a grid search comparing the number diagnoses per individual
in the simulation of the model and the dataset. See Figure S2 a-d for the
number of diagnoses per individual across 10-year age groups (0-9, 10-19,…)
from the dataset and the model result for 2004-2006 and 2012-2014.

We simulate the model for the calibration period spanning from 2003 to 2014.
During this calibration phase, the model computes, for each diagnosis group,
age group, and sex group, the discrepancies in the diagnosed cases between the
simulation result and data in age group $a$, referred to as $\delta d(a)$. The
first three ten-year age groups are combined into one age group (0-29 years),
the age groups 30-39 and 40-49 years are combined into one. The other age
groups remain 10-year age groups. This simplification is introduced because
the discrepancies among younger individuals grouped in ten-year age groups,
are too small in the case of specific diagnosis groups. The $\delta d(a)$
values are subsequently distributed annually, factoring in age and sex groups,
allowing for a refinement of the model and a more accurate representation of
disease dynamics. See Figure S1 for incidences in 2014 from the dataset
compared to the model result at the end of the calibration period, in 2014.

To distribute the discrepancies in diagnosed cases ($\delta d(a)$) across
diagnostic groups, age groups, and sex groups, from 2015 onwards, we employ a
rate calculation. Specifically, we determine a rate for each combination of
diagnosis, age-, and sex group. We use the geometric mean of the rates from
the data of the final three years of the calibration period, namely 2012,
2013, and 2014, for the forecast simulation period, spanning from 2015 to
2030.

###  2.3 Observables

We introduce several measures to describe the dynamics of the disease
trajectories. The relative incidence change ($\Delta I_{rel}$) of single
diagnose groups refers to the measure of how the incidence of a particular
diagnosis has changed in year $y+\Delta t$, relative to the initial incidence
in year $y$.

$\Delta I_{rel}=\frac{I_{y+\Delta t}-I_{y}}{I_{y}}$ (1)

To study the development of multimorbidity in terms of the number of diagnoses
received, we define multimorbidity incidence as the frequency of individuals
receiving $n$ diagnoses ($n$ = 1-3, 4-6, 7-9, >10). To study the development
of multimorbidity as specific disease patterns, we look at the relative
occurrence of a multimorbidity cluster, $c$, per year $y$, which is defined as
the ratio of transitions to cluster, $c$, to the total number of transitions
in that year.

The decrease in all-cause mortality (total number of deaths) due to reduction
of new-onset diagnoses is measured in reduction in death numbers and prevented
deaths per prevented diagnosis. We measure the reduction in death numbers by
comparing the total number of deaths in a simulation run where the new-onset
diagnoses of a particular diagnose group is reduced by a factor, $\gamma$, to
deaths due to all death causes in a simulation with no reduction. Prevented
deaths per prevented diagnoses are computed by dividing the total number of
deaths by the total number of reduced diagnoses for the simulation where a
certain diagnose group is reduced by a factor $\gamma$.

The impact of the Covid-19 Shock on the overall disease burden is estimated by
computing the difference in number of diagnoses from 2022-2030 between the
main and the respective Covid-19 Shock scenario, compared to the main scenario
(difference in incidence). Additionally, we compute the average years until
diagnosis and compare the Covid-19 Shock to the main scenario. This quantifies
how much earlier, on average, individuals are diagnosed with a diagnose group
as a result of the simulated Covid-19 Shock.

###  2.4 Scenarios

To assess the potential impact of interventions such as prevention efforts or
the introduction of new medications, we perform scenario simulations with
modified transition probabilities. In this framework, we annually reduce the
incidence of one of the 131 diagnostic groups, thereby allowing us to evaluate
the cumulative effects of these interventions over time. To reduce the
incidence of one diagnose, $d$, we reduce the transition probability
$q_{g,a,k,j}$, by multiplying it by a factor $\gamma$ (in our case
$\gamma=0.95$):

$\begin{split}q_{g,a,k,j}^{\prime}=(1-p_{j,d})q_{g,a,k,j}+\\\
p_{j,d}p_{k,d}q_{g,a,k,j}+\\\
(1-p_{k,d})p_{j,d}q_{g,a,k,j}\gamma\quad,\end{split}$ (2)

The first term in equation (2), refers to the transition probability of
individuals who will not be diagnosed with $d$ after transitioning from
cluster $k$ to $j$, the second term refers to the transition probability of
individuals already diagnosed with $d$ and the last term refers to the
transition probability (reduced by a factor $\gamma$) of individuals who would
be diagnosed with $d$ after transitioning to cluster $j$.

We estimate how the Covid-19 pandemic might affect the future incidence of
diagnoses and death numbers by implementing a "Covid-19 Shock". In the
Covid-19 Shock scenario, we assume that every person in Austria has been
infected with SARS-CoV-2 at least once by the year 2022. Subsequently, we
simulate the associated mortality resulting from post-acute sequelae of SARS-
CoV-2 infections based on empirical data [43]. To estimate the heightened
likelihood of individuals being diagnosed with specific diseases following a
SARS-CoV-2 infection, we employ Hazard Ratios (HR) reported in the
retrospective cohort studies (Table S1). To calculate this increased
probability, we analyze the frequency of diagnostic codes (per age- and sex
group) specified in the retrospective cohort studies within the 131 diagnostic
groups in the original dataset. Per age- and sex group, this frequency is then
multiplied by the probability assigned to each diagnostic group. The resulting
numbers are used to externally allocate the additional diagnoses within the
population. Subsequently, we assign new multimorbidity clusters to
individuals, taking into account all the diagnostic groups with which they
have been diagnosed. For the annual number of deaths, we take derived death
rates from the main scenario and multiply them by the number of diagnoses in
the Covid-19 Shock scenarios.

##  3 Results

###  3.1 Impact of aging population on disease burden

The out-of-sample simulation time span ranges from 2015 to 2030. Within this
period we evaluate predictions for annual changes in the incidence of the 131
diagnostic groups, thereby facilitating an exploration of the evolving disease
burden within the population. Figure 2a illustrates the relative change in
incidence ($\Delta I_{rel}$) between 2030 and 2015 for selected diagnoses
($\Delta I_{rel}$ > 13%) and Figure 2b the absolute incidence values for the
years 2015 (unfilled bars) and 2030 (filled bars). Increases in incidence are
observed for diseases affecting the nervous system, the genitourinary system
and the circulatory system. For other degenerative diseases of the nervous
system (G30-G32) we observe $\Delta I_{rel}$ = 32.04% (9.92), from 9,700
(9600) diagnoses in 2015 to 13,000 (1,300) in 2030. For malnutrition (E40-E46)
we find an increase of 24.49% (9.92), from 2,200 (13) diagnoses in 2015 to
2,800 (17) in 2030. For renal failure (N17-N19), $\Delta I_{rel}$ = 29.21%
(1.63), increasing from 36,000 (590) diagnoses in 2015 to 46,800 (760)
diagnoses in 2030. These are all diagnosis codes primarily prevalent in
elderly patients. Whereas a decrease in $\Delta I_{rel}$ by 18.50% (5.00),
from 15,800 (800) diagnoses in 2015 to 12,800 (640) in 2030, is visible for
diseases affecting younger individuals such as behavioral disorders and
diseases of the appendix (for information on incidence stratified by age, see
Figure S3).

For age-standardized incidence values, the age structure in 2030 is
standardized to the structure in 2015 (Figure 2c). An increase in age-
standardized incidence, such as for renal failure (N17-N19), from 2,900 (50)
diagnoses in 2015 to 3250 (50) in 2030, highlights that the changes in
incidence observed in the Figure 2a and b are not influenced by demographic
shifts (aging population) but by shifts in the overall health status of the
population.

Figure 2: Relative change in annual incidence of diagnose groups with a
relative absolute increase > 13 $\%$ 2030 compared to 2015 relative to 2015
(a). Absolute values of annual incidence for 2030 and 2015 (b). Increases in
annual incidence is primarily observed for fiseases affecting the nervous
system, the genitourinary system and the circulatory system as well as
malnutrition. Age standardized incidence in 2015 and 2030 (c). We assume the
same population structure in 2030 as in 2015. This shows, that for some
diagnose groups (i.e renal failure (N17-N19)) the model shows the change in
incidence not only due to a change in the population structure but also due to
a change in the health state of the population. In all panels, error bars
indicate the mean relative error from 2010 to 2014. We only show diagnosis
groups where we define a constant error (i.e. diagnose rates do not change
over time). We exclude all diagnosis groups where the absolute error in 2014
is greater than 5% of the incidence in 2014 and greater than 500 cases per
year, and all diagnosis groups where the error changes by 1.3 between 2010 and
2014.

The CDTM further allows us to examine the development of the frequency of
combinations of diagnoses from each multimorbidity cluster. Figure 3a offers
insight into the 20 most assigned multimorbidity cluster in 2015, comparing
the relative occurrence of these combinations in both 2015 and 2030. We show
the inclusion diagnoses per multimorbidity cluster. The most common
multimorbidity clusters are primarily those including hypertensive diseases.
This does not change during the forecast period. For the disease pattern
describing the co-occurrence of hypertensive diseases (I10–I15), other forms
of heart disease (I30–I52), diseases of arteries, arterioles and capillaries
(I70–I79) and renal failure (N17–N19) we find an increase in relative
occurrence from 1.73% to 3.0% from 2015 to 2030. The relative occurrence of
the pattern including hypertension, other forms of heart disease, organic,
including symptomatic, mental disorders (F00–F09) and renal failure, increases
from 1.13% to 2.14%. The third highest increase in relative occurrence from
2.40% to 3.32% is observed for hypertensive diseases, other forms of heart
disease and renal failure. Figure 3b contrasts the difference in this relative
occurrence between 2030 and 2015, stratified by gender. The difference in
relative occurrence between 2015 and 2030 varies for males and females mainly
in disease patterns including renal failure. For instance, males show an
increase of 1.70% and females an increase of 0.88% between 2015 and 2030 in
the disease pattern encompassing hypertensive diseases, other forms of heart
disease, diseases of arteries, arterioles, and capillaries, and renal failure.

Figure 3: Relative occurrence of the the 20 most common multimorbidity
clusters in 2015. Relative occurrence in the simulation year 2015 and 2030
(a). We show the inclusion criteria of all 20 multimorbidity clusters.
Especially clusters describing disease patterns containing hypertensive
diseases (I10-I15) exhibit an increase between 2015 and 2030. Difference in
relative occurrence 2030 compared to 2015 for females and males, respectively
(b). Difference in occurrence between male and females is only visible for
multimorbidity cluster including diseases of the genitourinary system.

###  3.2 Leverage points for optimal prevention schemes

Specific interventions can be expected to lead to decreases in incidence. In
the following, for each diagnosis, we evaluate how much a relative reduction
of 5% in the transition probabilities leading to new onsets of the diagnosis
impacts all-cause mortality, see Figure 4. We show the 10 diagnoses with the
largest effect on all-cause mortality only for potentially preventable
diseases (by medication, prevention efforts, vaccinations, etc.) (Figure 4 a).
These groups include C00-D49, E00-E99, F00-F99, I00-I99, J00-J99 and N00-N99.
We find the greatest reduction in deaths per diagnosis for diseases affecting
the circulatory system, neoplasms, endocrine, nutritional and metabolic
diseases, and diseases of the respiratory system. Each bar refers to the
average relative reduction in the number of deaths over a period of 15 years
per reduced diagnoses over 10 iterations due to a 5% reduction in the
transition probabilities of individuals who would be diagnosed with the
corresponding diagnosis on the y-axis.

For hypertensive diseases (I10-I15) we find a reduction of 0.57 (0.06)%, for
malignant neoplasms a reduction of 0.57 (0.07)% and for ischaemic heart
diseases (I20-I25) a reduction of 0.53 (0.04)% in all-cause mortality. These
diagnosis groups are the main causes of death in Austria [44]. Less important
causes of deaths are diseases of veins (I80-I89) (0.36 (0.06)%) and disorders
of the thyroid gland (E00-E07) (0.29 (0.05)%), suggesting that a reduction of
new onsets of diseases in these diagnose groups leads to a reduction in
potentially fatal sequelae.

To account for a potential bias due to differences in the incidence of the
reduced diagnose group and potential sequelae, we compute the ratio of
prevented deaths per prevented diagnose. Note that we do not just count the
prevented diagnoses of the diagnosis group on the y-axis, but include all
groups to account for the number of sequelae prevented. We find that there are
0.05 (0.01) prevented deaths per prevented diagnosis due to a reduction of 5%
of new onset malignant neoplasms, suggesting improvements in prevention of
malignant neoplasms as the optimal leverage point (Figure 4 b).

Figure 4: Effect of a 5% reduction in the transition probabilities leading to
new onsets of respective diagnosis groups. Reduction in overall death numbers
(all-cause mortality from 2022-2030) per reduced diagnosis of 10 diagnosis
groups with largest effect on all-cause mortality (a). Per diagnosis group,
$d$, on the y-axis we simulate a scenario where we annually reduce the
transition probabilities by 5% to clusters where the probability of being
diagnosed with $d$ in the following timestep increases. We compute an ensemble
average over 10 simulations. Error bars indicate the standard deviation over
these 10 simulations. Ratio of number of prevented overall deaths per
prevented overall diagnoses (b). To account for differences in the incidence
of both of the reduced diagnosis and potential sequelae, we show the number of
reduced deaths in relation to the number of reduced diagnoses (all diagnosis
groups) from 2022-2030.

###  3.3 Impact of post-acute Covid-19 sequelae on population health

As another example, we evaluate the impact of the Covid-19 pandemic on the
incidence rates of potential sequelae arising from SARS-CoV-2 infections,
along with consequential shifts in all-cause mortality. In the pessimistic
scenario 1, we reduce the HRs by 15%, and in scenario 2 by 40%. This reflects
the potential influence of less severe viral variants and future vaccination
campaigns. We analyze the difference in the total number of diagnoses
accumulated over nine years (all new onset diagnoses from 2022-2030) between
the baseline and Covid-19 Shock scenarios, compared to the baseline scenario
(Figure 5a), as well as the average time until diagnosis between the main and
the Covid-19 Shock scenarios (Figure 5b), serving as an indicator of expedited
diagnosis within the Covid-19 Shock scenarios.

The largest differences between the baseline and Covid-19 Shock scenarios are
observed for sequelae affecting the respiratory system, digestive system, and
mental, behavioral, and neurodevelopment disorders. For other respiratory
diseases (J95–J99), scenario 1 predicts 10,905 more diagnoses (equivalent to
0.13 diagnoses per 1,000 persons per year, based on the population in 2022
population [45]), while scenario 2 forecasts 7,684 additional diagnoses (0.09
diagnoses per 1,000 persons per year) compared to the baseline scenario. On
average, diagnoses occur 0.84 years earlier in scenario 1 and 0.82 years
earlier in scenario 2 than in the baseline scenario.

For respiratory diseases affecting the interstitium (J80–J84), scenario 1
shows 3,900 additional diagnoses (0.05 diagnoses per 1,000 persons per year)
and scenario 2 2,700 diagnoses (0.03 diagnoses per 1,000 persons per year)
more compared to the baseline scenario, with diagnoses occurring 1.12 and 0.85
years earlier, respectively. We find 15,300 more diagnoses (0.19 diagnoses per
1,000 persons per year) of diseases of the liver (K70–K77) in scenario 1 and
10,800 diagnoses more (0.13 diagnoses per 1,000 persons per year) in scenario
2, with diagnoses occurring 0.4 and 0.26 years earlier, respectively.

Organic, including symptomatic, mental disorders demonstrate 19,000 and 13,300
more diagnoses (0.23 and 0.16 diagnoses per 1,000 persons per year) in
scenarios 1 and 2, respectively. Diagnoses occur 1.06 and 0.81 years earlier
in scenario 1 and 2, respectively.

We examine the contrast in the number of fatalities recorded during the period
spanning 2022 to 2030 between the main and the two Covid-19 Shock scenarios
(see Figure S4). Notably, there is a rise in deaths attributed to
cerebrovascular diseases (I60–I69: 1147-819 deaths), ischaemic heart diseases
(I20–I25: 733-538 deaths), other mental and behavioral disorders (F00–F99:
434-291 deaths) and diabetes mellitus (E10–E14: 324-236 deaths) in response to
the Covid-19 Shock. In contrast, fatalities from malignant neoplasms exhibit a
reduction across in both Covid-19 Shock scenarios. This may be attributed to
individuals succumbing to alternative causes of death earlier in the
simulation.

Figure 5: Difference in the total number of diagnoses (from 2022 to 2030) of
the two Covid-19 Shock scenarios compared to the simulation without a shock,
respectively (a). Scenario 1 is the pessimistic scenario where we assume a 15
$\%$ reduction of the HR of the different diagnosis groups in the y-axis,
scenario 2 is the optimistic scenario where we assume a 40 $\%$ reduction of
due to less severe SARS-CoV-2 variants and vaccines. We find a modest impact
on the incidence of SARS-CoV-2 sequelae in both Covid-19 Shock scenarios.
Sequelae affecting the respiratory system and the digestive system are the
most affected diseases. Difference in the average years until the diagnosis
with and without Covid-19 Shock (b). This metric quantifies, how much earlier,
on average, are individuals diagnosed with each one of the diagnose groups on
the y-axis due to the Covid-19 Shock. The sequelae with the greatest
difference in average years until diagnose affect the respiratory, nervous and
circulatory system. In addition, organic, including symptomatic, mental
disorders (F00-F09) are diagnosed by up to one year earlier.

###  3.4 Model quality

Figure S1 represents the incidences of 131 diagnostic groups resulting from
both the simulation and the dataset at the end of the calibration period in
2014. We find good agreement between the annual incidences in the data and the
simulation with a Pearson correlation coefficient of $0.99$ across all
diagnoses.

Figure S2 shows a comparative analysis of the dynamics of multimorbidity
incidence between the simulation and the dataset. In addition, we present the
projection of multimorbidity incidence for the time span 2028-2030, derived
from the simulation results. In Figure S2, the number of individuals receiving
$n$ diagnoses is expressed as a percentage within each age group. Notably,
marginal fluctuations are observed in the evolution of the multimorbidity
incidence.

The model effectively captures the dynamics of multimorbidity among the
younger age cohorts (0-59). For the three oldest age groups ($\geq$ 60),
deviations from the empirical data become apparent when comparing the results
for 2012-2014 between the data and the model. In particular, the proportion of
highly multimorbid individuals (more than ten diagnoses) is overestimated by a
few percentage points in the model. In both, data and model, we see that the
distribution of the age-specific multimorbidity incidence remains fairly
robust over time, even in the projections until 2030.

We find that some diagnoses show a substantial inflation in the discrepancy
between data and simulation over time. There are 36 diagnostic groups with an
absolute error in 2014 exceeding 5% of the 2014 incidence and surpassing 500
cases per annum, as well as those manifesting a 1.3-fold error increase from
2010 to 2014. These diagnoses are excluded from further analysis of changes in
incidence.

##  4 Discussion

We generalize compartmental models as used in epidemiology for modeling
infections diseases in a way that they can be used for long-term predictive
modeling of chronic diseases. The main idea behind it is to reconstruct
individual chronic disease trajectories between different sets of pathological
conditions that are represented as "compartments".

The essence of the model is that it can be fully calibrated from actual
nationwide observational data. We present a realization of the model that is
based on an extensive dataset of hospital diagnoses in Austria from 1997 to
2014. We simulate demographic changes (births, migration, deaths) and the
acquisition of new diagnoses based on a multimorbdity network. We calibrate
the model within the period 2003-2014 and forecast changes in the incidence of
131 diagnostic groups and combinations thereof from 2015 to 2030. To our
knowledge, the CDTM is the first of its kind by encompassing 131 diagnostic
groups spanning diseases from A00-N99 across all age groups. This
comprehensive microsimulation framework allows for realistic projections of
the incidence of individual diseases and multimorbidity. Additionally, it
offers a valuable framework for evaluating the ramifications of various
scenarios on the disease burden within the population, such as prevention
efforts, new medication or new diagnostic techniques. We identify diagnoses
which, when targeted with prevention efforts could decrease all-cause
mortality and promote healthy aging in an optimal way.

In our baseline scenario, where we simulate the projected changes in births,
migration, and deaths as forecasted by the national statistics office, without
considering alterations in mortality rates, diagnostics, etc., we observe a
relative increase in the incidence of chronic diseases affecting the nervous
system, genitourinary system, metabolic diseases, and those impacting the
cardiovascular system. In Figure S3, the relative incidence stratified by
above/below 65 shows that these diagnoses are more common among individuals
above 65. In contrast, the diagnose groups where we observe a decrease in
relative incidence, behavioral disorders with onset in childhood (F90-F98) and
diseases of appendix (K35-K38) are more common among individuals under 65.

The model allows us to examine not only changes in the annual incidence of
individual diagnoses, but also changes in the incidence of multimorbidity
patterns over time. We observed that the 20 most common multimorbidity
clusters that individuals transitioned to in 2015 all showed an increase in
relative occurrence (transitioning from one cluster to another) in 2030. 18
out of the 20 most common clusters describe disease patterns including
hypertensive diseases (I10-I15), among these are also the most pronounced
increases from 2015 to 2030 such as a disease pattern describing hypertensive
diseases (I10-I15), other forms of heart disease (I30-I52) and renal failure
(N17-N19). This finding is in line with existing literature, which
consistently identifies hypertension as one of the most prevalent chronic
conditions, either in isolation or in combination with other chronic
conditions such as diabetes, hyperlipidemia, ischemic heart disease and
chronic kidney disease [46, 47, 48].

The CDTM now enables us to provide concrete quantitative estimates for the
future development of such multimorbidity clusters under certain conditions.
From 2015 to 2030, an average increase of 0.7% in the occurrence of clusters
where individuals have at least four diseases is expected. This means that by
2030, 20,700 more individuals will transition to a cluster describing a
disease pattern encompassing four or more diseases compared to 2015. This
indicates a notable escalation in the complexity of health conditions within
the population, suggesting a heightened disease burden that may necessitate
more comprehensive healthcare management strategies.

Healthcare costs of multimorbidity are difficult to estimate, as the costs of
single diseases are not necessarily additive and are likely to depend which
diseases co-occurr [49]. Using estimates from a systematic review on the costs
of multimorbidity and our results on the occurrence of multimorbidity clusters
we can approximate an the expected cost increase for selected multimorbidity
clusters. We estimate increased costs of I$ 8.7 million (95% CI: I$ 8.5
million - I$ 8.9 million) for hypertensive diseases and dorsopathies and I$
29.8 million (29.1 million-30.5 million) for hypertensive diseases and
arthropathies (average annual direct medical costs of I$ 13,300 (13,000-13,600
95% CI) for hypertension and musculoskeletal disorders) in 2030 compared to
2015. For hypertensive diseases and diabetes mellitus we estimate an increase
of I$ 13.1 million (12.8 million-13.5 million) (average annual direct medical
costs of I$ 14,300 (13,900-14,700) for hypertension and type 2 diabetes) and
an increase of I$ 37.2 million (36.4 million -38 million) for hypertensive
diseases and other forms of heart disease (I$ 17,900 (17,500-18,300) for
hypertensive diseases and heart/vascular conditions) [49].

The largest differences in the relative occurrence increase between men and
women is observed in disease patterns involving renal failure, with men
experiencing a larger increase. This aligns with existing literature
indicating that while chronic kidney disease (CKD, N18) is more prevalent
among women, the combination of CKD with cardiovascular diagnoses is more
commonly observed among men [50, 51].

Using the novel model, we develop a framework to study the effectiveness of
mitigation efforts (such as vaccinations or other preventive measures) in
reducing causes of death. For each diagnosis, to mimic a prevention measure,
we impose a 5% reduction in the transition probability for each individual who
would be diagnosed in the following timestep with the respective diagnosis. We
also reduce the externally imposed incidence of that diagnosis by 5%. We find
the largest reduction in deaths for each prevented diagnose for diseases
affecting the circulatory system (hypertensive diseases (I10-I15), ischaemic
heart diseases (I20-I25), cerebrovascular diseases (I60-I69) and diseases of
veins (I80-I89)), malignant neoplasms (C00-C97), endocrine, nutritional
diseases (metabolic disorders (E70-E90), diabetes mellitus (E10-E14) and
disorders of the thyroid gland (E00-E07)) and diseases of the respiratory
system (acute respiratory infections (J00-J06)). We find that prevention
efforts regarding these diagnoses have the potential to effectively promote
healthy aging most optimally.

At a global level, high blood pressure was the 6th leading risk factor for
disability-adjusted life years (DALYs) in women in 1990 and had risen to be
the leading risk factor for women by 2019, followed by high fasting plasma
glucose and high body mass index, thus representing the full spectrum of the
metabolic syndrome [52]. In men, smoking was the third leading risk factor in
1990 and had risen to be the leading risk factor for by 2019, followed by high
blood pressure and high fasting plasma glucose. In Austria, hypertension moved
to the leading risk factor for DALYs in women, followed by smoking and high
body-mass index. Smoking is the leading risk factor in men in Austria,
followed by high blood pressure and alcohol use [52]. More than half of the
population over the age of 60 suffer from increased blood pressure with many
patients undetected and/or undertreated [53]. Hypertension relates to many
other severe diseases and in combination with obesity, greatly increases the
risk of heart failure and, in the presence of concomitant diabetes even more
renal disease and vasculopathy [54]. Therefore, many diseases including
cardiometabolic disorders could indeed be prevented by better screening, early
diagnosis and better treatment of modifiable risk factors like blood pressure,
LDL cholesterol, glucose and body weight and prevention of obesity, diabetes
and hyperlipidemia [55, 56]. Many studies have shown that the majority of
patients do not reach their target levels even under medication, probably
because of drug side effects, lack of adherence or clinical inertia [57, 58,
59, 60].

Reducing smoking, especially among women, and alcohol consumption, especially
among men, would also help to reduce multimorbidity and increase life
expectancy in Austria [9]. In fact, the incidence of vascular diseases and
many types of cancer could be reduced or prevented by increased public health
efforts with a special focus on the prevention of infections, obesity, alcohol
and smoking [55]. In addition, new and more effective drugs that reduce
hyperglycaemia and obesity and additionally reduce the risk of cardiovascular
disease, heart failure and renal failure, such as GLP-1 RA and SGLT2
inhibitors, could help to reduce multimorbidity and premature mortality in the
future [61]. New lipid-lowering drugs with low adverse events and easy long-
term use could also help reduce vascular and possibly neurodegenerative events
[62]. We did not see a large effect of sex on our results of the development
of multimorbidity patterns. Men show a slightly greater increase in morbidity
and mortality due to renal failure. In fact, men are more likely to be on
haemodialysis, although women are more likely to have mild or moderate renal
impairment. Better screening for kidney disease and treatment of diabetes and
vascular problems will reduce the risk of kidney failure in older people.

An interesting observation was that reduction of thyroid diseases would have
great impact on reduction of multimorbidity and death rates. Thyroid
dysfunctions particularly hypothyroidism are very common especially in women.
These disorders can be easily detected and treated in most cases. Thyroid
hormones are essential for controlling body temperature, energy expenditure
and cardiometabolic function. Associations between thyroid function and
arrhythmias are well known and a thyroid-cardiac axis has been proposed, which
may explain the clinical observation of an association between thyroid
function and mortality [63]. Hyperthyroidism and thyreotoxicosis can
dramatically increase mortality risk [64]. Both hypothyroidism and
hyperthyroidism have been associated with an increased risk of cardiovascular
morbidity and mortality in epidemiological studies and meta-analyses. There
are several possible pathophysiological mechanisms linking thyroid and
cardiovascular disorders such as endothelial dysfunction, blood pressure
changes, dyslipidemia, and low-grade systemic inflammation [65].

Venous disorders (I80-I89) are, like disorders of the thyroid gland a less
common causes of death. However, they are common, especially in women, and
represent a large health care burden. Our analysis revealed that a reduction
of new onsets of diseases of veins leads to a reduction in potentially deadly
sequelae. Venous disorders comprise conditions of varying severity and
pathology, including venous thromboembolic disorders resulting from
dysregulated coagulation as well as chronic venous disease resulting from
tissue damage due to prolonged venous hypertension [66]. However varicose
veins also dramatically increase the risk of deep venous thrombosis. In
addition, the postthrombotic syndrome affects up to 60% of patients with deep
venous thrombosis. In recent decades, there has been a steady increase in
thromboembolic events, including pulmonary embolism, with high rates of
recurrence and increased risk of mortality [67]. There are multiple risk
factors such as increased age, obesity, prolonged immobility, fractures,
hospitalisations and conditions associated with impaired haemostasis such as
cancer, diabetes, autoimmune diseases and infections including Covid-19 and
pregnancy. It is therefore plausible that a greater focus on possible
preventive measures and the reduction of venous disease could imply a large
reduction in healthcare costs and morbidity.

As a further demonstration of the versatility of the compartmental disease
trajectory model (DCTM), we implement a Covid-19 Shock to estimate the long-
term health impact of the Covid-19 pandemic on the Austrian population for
both, a pessimistic and an optimistic scenario. Using hazard ratios for being
diagnosed with certain sequelae of a SARS-CoV-2 infection drawn from multiple
respective cohort studies (see table S1), we study the relative incidence
difference of the baseline scenario and the two Covid-19 Shock scenarios. We
find the most pronounced increase in incidence (2022-2030) compared to the
baseline scenario for other respiratory diseases (43.12-56.17% and
7,700-10,900 diagnoses), for respiratory diseases affecting the interstitium
(43.81-55.88% and 2,700-3,900 diagnoses), diseases of the liver (32.13-42.32%
and 10,800-15,300 diagnoses) and organic, including symptomatic, mental
disorders (28.75%-36.48% and 13,300-19,000 diagnoses). This aligns with our
approach, as these sequelae are associated with the highest Hazard Ratios
(HRs), except for diseases of the liver. This suggests that the increase in
relative incidence of liver diseases is not solely a direct effect of the
Covid-19 shock but may also be attributed to it being a sequelae of one of the
other conditions. A study of the costs of multimorbidity found average annual
direct medical costs of I$ 36,800 (36,400-37,300) for respiratory and mental
health conditions and I$ 35,000 (34,900-35,300) for respartory and
heart/vascular conditions [49]. We find that on average, individuals are
diagnosed with organic, including symptomatic, mental disorders 0.8-1.1 years
earlier in Covid-19 Shock scenarios 2 and 1 compared to the baseline scenario.
For respiratory diseases affecting the interstitium, individuals are diagnosed
up to 0.9-1.1 years earlier. This could potentially lead to an accumulation of
more diagnoses as multimorbidity is more compressed towards older ages in
simulations without the Covid-19 Shock.

The present study is subject to several limitations. One is limitations in
data availability. The hospitalization dataset contains only information until
up to 2014 and recent changes, such as medical advances concerning certain
diseases, new medication or improvements in diagnostics are not covered. We
partially mitigate this issue by evaluating the change in incidence of
diagnoses without an error inflation over time, i.e. the difference between
data and model incidence (the error) is not changing (in- or decreasing) by
more than 1.3 in the last five years of the calibration phase. Another
limitation is that it is not possible to distinguish from the data whether a
patient did not require further hospitalizations for medical reasons or
discontinued his or her treatment for other reasons. The model only examines
cumulative health states. It is however reasonable to assume that, especially
severe, chronic diseases affect the health state of a patient on a long-term
basis. Another shortcoming is the lack of information on outpatient contacts,
doctor visits, diagnoses for deaths outside the hospital, socio-economic
status and prescribed medications is not available. Finally, the dataset was
originally collected for billing purposes, which leads to a potential bias in
terms of over- or under-representation of diagnoses.

Data on births, migration, deaths and causes of death are provided by official
statistics, ’Statistics Austria’. The forecasts on number of births, migration
and deaths (2022 onwards) are taken from the main scenario of Statistics
Austria. Data on causes of death are only available up to 2019. We assume that
the distribution of death numbers across the different causes remains constant
after 2019. Therefore the model doesn’t capture changes in death rates by
cause. In addition, the projected number of deaths from 2019 onwards assumes
the age and sex distribution of deaths by cause in 2019, as the projected
number of deaths, stratified by age and sex, are only available for scenarios
that already include the effect of the Covid-19 pandemic. This means that the
model accurately captures the total number of deaths, but it does not take
into account the different trends in the age and sex distributions.

On a methodological level, we make two important adjustments to the
multimorbidity network by Haug et al. (2020) [22]. First, we compute new
probabilities of being diagnosed with disease, $d$, given an assignment to
cluster, $c$, to calibrate the model at initialization to the incidences in
the data in 2003. Second, we rescale the age- and sex-dependent transition
probabilities overall (same scaling factor for each diagnosis) by an age-
dependent factor $\alpha$, simulate from 2003-2014 and externally assign the
difference per age-, sex- and diagnose group to calculate rates for the
forecast period. Using the transition probabilities without adjustment does
capture the development of incidence per diagnosis group in the calibration
period 2003-2014. However, the use of unadjusted transition probabilities
results in the model not correctly capturing the dynamics of multimorbidity
(number of individuals diagnosed with 2 or more diseases) in the data. Note,
that our population cohort differs from the cohort used to construct the
network in [22], which consisted of individuals with no recorded diagnoses in
1997-2002. The population cohort studied here includes these individuals,
hence adjustments in the transition rates are necessary.

The implementation of the Covid-19 Shock relies on assumptions taken over from
the literature. These should be considered when interpreting the results. We
assume, that each individual in the model population has been infected once by
2022. The HRs used are from different retrospective cohort studies [68, 69,
70, 71] which were mainly conducted early-on in the pandemic. Therefore, we
assume a reduction of the HRs by 15% (scenario 1) and 40% (scenario 2) due to
less severe virus variants and vaccination rollouts, respectively. We provide
an estimated range of the impact of the pandemic on the healthcare burden and
not exact incidence forecasts. Further studies on sequelae of SARS-CoV-2 can
be used to make more precise estimates on how the Covid-19 pandemic affects
the healthcare system in terms of chronic disease incidence and
multimorbidity.

Additional research is required to investigate the progression of
multimorbidity, particularly in the context of an aging population and
socioeconomic factors. It has been found that the onset of multimorbidity
occurs 10 to 15 years earlier for people living in socioeconomically
disadvantaged regions [72, 73]. Applying the presented CDTM approach to a
different country is not only essential for validation but also facilitates
the discernment of disparities in multimorbidity attributed to variations in
healthcare systems and the overall health status of the population.
Furthermore, it would be of great interest to study the impact of different
shocks on the burden of disease, such as heat waves or other climate change-
related scenarios.

### Author Contributions

PK conceptualized and supervised the project. PK and KL devised the analytic
methods. KL carried out the analysis and produced the plots and graphics. KL
and PK wrote the first draft of the manuscript. AK-W and ST made critical
comments regarding the manuscript. AK-W contributed medical expertise
regarding the medical interpretation of the findings and in developing medical
hypotheses. AK-W, ST, KL and PK conducted reviewing and editing of the
manuscript. All authors read and approved the final manuscript.

### Data Availability Statement

This study was conducted using a pseudonymized research dataset only
accessible for selected research partners under strict data protection
regulations. Data on disease cluster and sex- and age-stratified transition
rates between the different clusters is available from the authors upon
request.

### Competing Interests Statement

The authors have declared that no competing interests exist.

### Code Availability

The underlying code for this study [and training/validation datasets] is not
publicly available but may be made available to qualified researchers on
reasonable request from the corresponding author.

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## Supplementary Information

Figure S1: Incidence of the 131 diagnose groups in simulation year 2014 and incidence of the 131 diagnose groups in the data, 2014.  Figure S2: Multimorbidity Incidence observed in the dataset and the simulation results. Each figure shows the proportion of individuals with k diagnoses (ranging from 1-3 to more than 10 diagnoses) among all individuals being diagnosed with at least one diagnose in the respective age groups. The figures a) and b) in the top panel show the incidence of multimorbdity in the dataset for the periods 2004-2006 and 2012-2014, respectively. In the bottom panel, the figure c), d) and e) show the multimorbidity incidence in the simulation result for the time periods 2004-2006, 2012-2014 and 2028-2030, respectively. Comparing a) and c), and b) and d) shows that the model represents the multimorbdity trends well in the younger age groups (from 0 to 59). The model shows deviations from the resulting incidence in the data in respect to the last three age groups, especially for individuals aged 80 years or older. The proportion of individuals in the simulation result with 1-3 diagnoses in the first six age groups ranges from 93 $\%$ for individuals aged 20-29 to 74 $\%$ for individuals aged 50-59 for the time period 2004-2006. In the dataset, we observe 95 $\%$ for individuals aged 20-29 to 76 $\%$ for individuals aged 50-59. The mean absolute deviation for all k diagnoses in these age groups is 1$\%$. For individuals aged 60 years or older the proportion of individuals with 1-3 diagnoses ranges from 66 $\%$ to 68 $\%$ in the simulation result and 68 $\%$ to 50 $\%$ in the dataset. The mean absolute deviation for all k diagnoses in these age groups is 6 $\%$. The simulation yields among the first six age groups a range of proportion of individuals with 1-3 diagnoses from 91 $\%$ (20-29 years) to 68 $\%$ (50-59 years) in the time period 2014-2016. In the dataset we observe 95 $\%$ (20-29 years) to 81 $\%$ (50-59 years) for the same timeframe. The mean absolute deviation for all k diagnoses in these age groups is 3 $\%$. For the last three age groups the simulation results in a proportion of individuals with 1-3 diagnoses ranging from 61 $\%$ (60-69 years) to 71 $\%$ (>= 80 years) whereas in the data we find a range from 74 $\%$ (60-69 years) to 59 $\%$ (>= 80 years). The mean absolute deviation for all k diagnoses in these age groups is 6 $\%$.  Figure S3: Relative incidence in 2014 (from dataset) of the diagnoses shown in Figure 2. Relative to number of individuals diagnosed in that year (stratified by younger or older than 65).  Disease | Disease Group | Hazard | Source
---|---|---|---
|  | Ratio |
Anxiety Disorder | Neurotic, stress-related and somatoform disorders (F40-F48) | 1.38 | [70]
Depressive Disorder | Mood [affective] disorders (F30-F39) | 1.44 | [70]
Ischemic stroke | Cerebrovascular diseases (I60-I69) | 1.5 | [70]
Myocarditis | Other forms of heart disease (I30-I52) | 5.38 | [68]
Myocardial Infarction | Ischaemic heart diseases (I20-I25) | 1.63 | [68]
Angina | Ischaemic heart diseases (I20-I25) | 1.52 | [68]
Heart Failure | Other forms of heart disease (I30-I52) | 1.62 | [68]
Non-ischemic Cardiomyopthy | Other forms of heart disease (I30-I52) | 2.45 | [68]
Cardiac Arrest | Other forms of heart disease (I30-I52) | 2.43 | [68]
Pulmonary Embolism | Pulmonary heart disease and | 2.93 | [68]
| diseases of pulmonary circulation (I26-I28) |  |
Migraine | Episodic and paroxysmal disorders (G40-G47) | 1.21 | [70]
Peripheral Neuropathy | Polyneuropathies and other disorders | 1.34 | [70]
| of the peripheral nervous system (G60-G64) |  |
Encephalopathy | Other disorders of the nervous system (G90-G99) | 1.82 | [69]
Seizure | Episodic and paroxysmal disorders (G40-G47) | 1.8 | [70]
Dementia | Other degenerative diseases of the nervous system (G30-G32) | 4.00 | [69]
| Organic, including symptomatic, mental disorders (F00-F09) |  |
Type 2 Diabetes | Diabetes mellitus (E10-E14) | 1.4 | [71]
Liver Test Abnormality | Diseases of liver (K70-K77)& Diseases of veins, lymphatic vessels and | 1.70 | [69]
| lymph nodes, not elsewhere classified (I80-I89)& Viral hepatitis (B15-B19) |  | [69]
Kidney Injury | Hypertensive diseases (I10-I15)& Renal failure (N17-N19) | 1.53 | [69]
Respiratory Failure | Other diseases of the respiratory system (J95-J99) | 3.67 | [69]
Interstitial Lung Disease | Other respiratory diseases principally affecting the interstitium (J80-J84) | 7.00 | [69]
Atopic Dermatitis | Dermatitis and eczema (L20-L30) | 1.11 | [69]
Urticaria | Urticaria and erythema (L50-L54) | 1.40 | [69]
Herpesviral vesicular dermatitis | Viral infections characterized by skin and mucous membrane lesions (B00-B09) | 1.43 | [69]
Sleep Apnea | Episodic and paroxysmal disorders (G40-G47) | 1.75 | [69]
Transient ischemic attacks | Episodic and paroxysmal disorders (G40-G47) | 1.62 | [70]
Hemorrhagic stroke | Cerebrovascular diseases (I60-I69) | 2.19 | [70]
Cerebral venous thrombosis | Cerebrovascular diseases (I60-I69) | 2.69 | [70]
Alzheimer | Other degenerative diseases of the nervous system (G30-G32) | 2.03 | [70]
Dysautonomie | Other disorders of the nervous system (G90-G99) | 1.3 | [70]
Bells palsy | Nerve, nerve root and plexus disorders (G50-G59) | 1.48 | [70]
Stress and adjustment disorder | Neurotic, stress-related and somatoform disorders (F40-F48) | 1.39 | [70]
Psychotic disorder | Schizophrenia, schizotypal and delusional disorders (F20-F29) | 1.51 | [70]
Joint pain | Arthropathies (M00-M25) | 1.34 | [70]
Myalgia | Soft tissue disorders (M60-M79) | 1.83 | [70]
Myopathy | Diseases of myoneural junction and muscle (G70-G73) | 2.76 | [70]
Guillan Barre Syndrome | Polyneuropathies and other disorders | 2.16 | [70]
| of the peripheral nervous system (G60-G64) |  |
Transverse Myelitis | Demyelinating diseases of the central nervous system (G35-G37) | 1.49 | [70]
Cholangitis | Disorders of gallbladder, biliary tract and pancreas (K80-K87) | 2.02 | [74]
IBS | Other diseases of intestines (K55-K63) | 1.54 | [74]
Acute Gastritis | Diseases of oesophagus, stomach and duodenum (K20-K31) | 1.47 | [74]
Functional Dyspepsie | Diseases of oesophagus, stomach and duodenum (K20-K31) | 1.36 | [74]
Acute Pancreatitis | Diseases of oesophagus, stomach and duodenum (K20-K31) | 1.46 | [74]
GERD | Diseases of oesophagus, stomach and duodenum (K20-K31) | 1.35 | [74]
PUD | Diseases of oesophagus, stomach and duodenum (K20-K31) | 1.62 | [74]
Table S1: Hazard Ratios of diagnoses affected by Covid shock simulation.
Figure S4: Impact of the Covid Shock Scenarios on death numbers. The figure
illustrates the difference in death numbers from 2022 to 2030. There is an
increase especially in death causes related to diseases affecting the
circulatory system. We observe a decrease in deaths due to malignant
neoplasms. This can be attributed to individuals succumbing to other diseases
earlier in the simulation.  Figure S5: Impact of the Covid Shock Scenarios on
multimorbidity pattern occurrence. We show the 20 most common mutlimorbidity
cluster transitioned to in 2030 in the Covid Shock Scenario 1 (pessimistic
scenario) and compare the relative occurrence for the standard scenario and
both Covid Shock scenarios.