Changing of Spreading Dynamics for Infectious Diseases in an Aging

Society: A Simulation Case Study on Flu Pandemic

Ting-Yu Lin

, Wei Ping Goh

, Hung-Jui Chang

, Mei-Lien Pan

, Shu-Chen Tsai

, Da-Wei Wang

and

Tsan-Sheng Hsu

1, ∗

Institute of Information Science, Academia Sinica, Taiwan

Department of Applied Mathematics, Chung Yuan Christian University, Taiwan

{mlpan66, pabeni, wdw, tshsu}@iis.sinica.edu.tw

Keywords:

Agent-based Simulation, Flu Pandemic, Aging Society.

Abstract:

In this paper, we report some initial results obtained from the agent-based simulation system SimTW about the

changing of spreading dynamics, e.g. speed, magnitude and affected people of different ages, when the target

society is aging. A disease model of inﬂuenza is built and then is invoked with two different social structures,

e.g., population and household distribution, and working and schooling patterns based on Census 2000 and

Census 2010 of Taiwan. In the 10 years time, the average population age in the country increases from 33.0

to 37.6 while the average household size decreases from 3.19 to 2.94. From the simulation results, we ﬁnd

that in the more aging year-2010 society, the pandemic, if occurred, is smaller, in terms of the total number of

infected persons and slower in terms of the date of the peak number of daily new cases, but is more serious

both in terms of the numbers of needed hospital beds and death cases. Using this ﬁnding, we hope to motivate

further discussions on adapting public health policies to this inevitable global trend of aging.

1 INTRODUCTION

The building of an agent-based simulation on model-

ing the spreading of infectious diseases like inﬂuenza

or ﬂu has been reported in order to study their spread-

ing dynamics (Adam, 2020; Tsai et al., 2010). We

observed from the kernel of simulation systems that

vital factors affecting the nature of spreading include

the compositions of people in households, communi-

ties, work groups and schools. In a typical scenario,

virus in an infected person travels through commut-

ing to work places and schools. The virus also has a

better chance of propagating in households of larger

sizes. Motivated by these observations, and the fact

that the world is aging with a growing average popu-

lation age and smaller household size (World Health

Organization, 2020), we want to study and compare

disease spreading patterns between two societies with

different aging populations. We hope to study chang-

ing of spreading patterns and as a result to motivate

better adaptation of public health policies reﬂecting to

inevitable demographical changes over time. In order

not to deal with parameter aligning across different

∗

Corresponding author.

societies, we choose to carry the study on the same

society, but with a 10-year time-lag. That is, we com-

pare the results between the demography of Taiwan in

the year 2000 and that of the year 2010. We also fo-

cus on ﬂu which one of the most common infectious

diseases (Riley, 2007).

In this paper, we study the spreading patterns be-

tween the two populations in year-2000 and year-

2010 respectively in Taiwan on inﬂuenza pandemic

and discuss medical resources requirements if it oc-

curred. We ﬁrst generate mock populations of year-

2000 and year-2010 based on Taiwan census data in

years 2000 and 2010 (National Statistics, ROC (Tai-

wan), ). Then we use the disease nature history pa-

rameters and system parameters as given in SimTW

(Tsai et al., 2010). We then perform simulations on

the two models and collect the data on daily newly

infected cases. The risk level of people with differ-

ent ages are different for a disease like ﬂu if infected.

Using parameters reported in (Meltzer et al., 1999),

we calculate the total hospital beds needed and the

death toll. From the simulation results, we ﬁnd that

in the more aging year-2010 society, the pandemic, if

occurred, is smaller, in terms of the total number of

infected persons and slower, in terms of the date of

Lin, T., Goh, W., Chang, H., Pan, M., Tsai, S., Wang, D. and Hsu, T.

Changing of Spreading Dynamics for Infectious Diseases in an Aging Society: A Simulation Case Study on Flu Pandemic.

DOI: 10.5220/0010618204530460

In Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2021), pages 453-460

ISBN: 978-989-758-528-9

453

the peak number of daily new cases, but is more seri-

ous both in terms of the numbers of needed hospital

beds and death cases. Using this ﬁnding, we hope to

motivate further discussions on adapting public health

policies to this inevitable global trend of aging.

The structure of the rest of this paper is as follows.

In Section 2, we give a survey of related work. In Sec-

tion 3, we describe our data source and the methods

we used. In Section 4, we describe the experimental

results. In Section 5, we give some discussions. Fi-

nally, in Section 6, we give some possible future work

and conclusions.

2 RELATED WORKS

Simulation models has been widely used in many

ﬁelds such as epidemiology (Ferguson et al., 2006)

and weather forecast (Furrer and Katz, 2008) as an ef-

fective tool to understanding characteristic of disease

and predicting the future.

The pace of population aging around the world is

increasing dramatically. Taiwan became an aging so-

ciety in 1993, an aged society in 2018 and will be-

come a super aged society in 2025 as projected in

(World Health Organization, 2020; Taiwan, National

Development Council, Executive Yuan, 2020). A dis-

ease has different impacts on different age groups.

For example, the death rate of covid 19 among peo-

ple 70 years older is 100 times more than that of the

age group between 20 and 30 years old (Bialek et al.,

2020; Richardson et al., 2020; Tsay et al., 2020).

There are two main approaches for simulation

work done for epidemiology studies, namely a math-

ematical one and an agent-based one.

Agent-based stochastic simulation is an approach

that widely used for studying infectious diseases

(Germann et al., 2006). This approach can be seen as

a real world environment that has been simpliﬁed and

modularized. We can do a lots of experiments that

hard to do in real life and get some useful insights

from the results. For example, (Tsai et al., 2010)

helped government designed intervention methods to

prevent the spread of diseases and (Chang et al., 2015)

study about the impact of household structure on epi-

demiology.

In a mathematical modeling of infectious dis-

ease, the sensitivity analysis is employed to aid in

identifying inﬂuential model parameters (Wu et al.,

2013). Many domains which utilize simulation soft-

wares have recognized the importance of validation,

veriﬁcation, and uncertainty quantiﬁcation of simula-

tion outcomes to build trust in interpreting generated

results for decision-making processes (Wright et al.,

2020). Relatively few work has been reported on

this regard when agent-based disease simulations are

used(Venkatramanan et al., 2018; Hunter et al., 2018;

Perkins et al., 2019; Hoertel et al., 2020; Ferguson

et al., 2020).

3 MATERIAL AND METHOD

In this section, we ﬁrst describe our data source. Then

we describe the architecture of the agent-based simu-

lation system called SimTW that we used. Finally, we

give the experimental designs and parameters.

3.1 Data

We brieﬂy describe the difference between the year-

2000 and year-2010 societies. The difference in age

distribution and household size between year-2000

and year-2010 are shown in Table 1 and Figure 1.

The population size of year-2000 is about 22.27 mil-

lion and year-2010 is about 23.16 million. In Fig-

ure 1, the percentage of population below 25 years

old drops about 8.7% from year-2000 to year-2010,

but the above-45-years-old population increases about

10.5%. The average population age of year-2000 is

33.0 years old and year-2010 is 37.6 years old which

means that the whole population in year-2010 is much

older than that of year-2000.

Household structure is one of the important fac-

tors affects the disease transmission network (Chang

et al., 2015). Figure 1 shows the percentages of

household sizes from 1 to 8 member in years 2000 and

2010. The total number of households increases from

6.38 million to 7.85 million and the average drops

from 3.19 to 2.94. The number of households contain-

ing at least 5 members about decreases signiﬁcantly.

Figure 1: Percentage of household sizes from 1 to 8 member

in year-2000 and year-2010.

3.2 Simulation System

In this paper, we used the simulation software devel-

oped by (Tsai et al., 2010). This software implements

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

454

Table 1: Population distribution of year-2000 and year-2010 in ﬁve age groups.

0-4 5-19 20-29 30-64 65+ all

year

2000

number of

people

1,489,242 5,089,214 3,780,665 9,996,243 1,921,308 22,276,672

percentage 6.69% 22.85% 16.97% 44.87% 8.62%

average population

age = 33.03

year

2010

number of

people

964,093 4,268,372 3,473,436 11,968,329 2,487,893 23,162,123

percentage 4.16% 18.43% 15.00% 51.67% 10.74%

average population

age = 37.62

an agent-based stochastic and heterogeneous discrete

time agent-based model.

3.2.1 Mock Population

This software generates a mock population. i.e., the

set of agents, based on the national demographics, and

then build daily commuting pattern, i.e., worker and

student ﬂow, using Taiwan Census Data Year 2000.

Each agent in this system has its own attributes, such

as person ID, age group, gender, routine type, resident

place, work/school place, medical record and so on.

This system uses an approach proposed by (Geard

et al., 2013) to generate a mock population with

household structure. It separates the whole popula-

tion into ﬁve age groups, namely preschooler children

(0-4 years old), school-age children (5-18 years old),

young-adults (19-29 years old), adults (30-64 years

old) and elders (65+ years old). People in the same

age group has similar behaviors such as daily activi-

ties and contacts. Routine type is an attribute that de-

scribes an individual’s activities. There are nine types

in the model: household, day-care center, play-group

children, kindergarten student, elementary school stu-

dent, middle school student, high school student, uni-

versity student and workers.

3.2.2 Social Structures

A mixing group is a daily close association of in-

dividuals, where every member is connected to all

other members in the same group. There are twelve

classes of such mixing groups in the model and they

can be divided into three categories: resident areas,

routine areas and surrounding areas. Resident areas

include household, household cluster, day-care cen-

ter and play-group which is the location of the agent’s

home. Routine area is where agents stay for working

and studying which include kindergarten, elementary

school, middle school, high school, university, work

group, dormitory of university and dormitory of work

group. Surrounding area are neighborhood and com-

munity which represented the places providing occa-

sional casual association such as shopping mall and

restaurant around university.

3.2.3 Agent’s Behavior

Each simulation day is set as workday, holiday

or long holiday which is a holiday lasts for more

than 2 days according to the calendar publish by

(Directorate-General of Personnel Administration,

Executive Yuan, ROC (Taiwan), ). Each day is di-

vided into the day time and the night time period

with 12 hours each. Agents go to their routine ar-

eas in the daytime of a workday except non-schooling

preschooler children, dropped out school-age children

and young-adults, adults and elders if unemployed

and non-schooling. During the night time of workday

and the whole day in a holiday, agents who commute

to routine area stay at resident area. Those who stay

in dormitories go to their resident areas only during

long holidays.

3.2.4 Disease Transmission Model

We use the SEIR disease model as described in

(Krumkamp et al., 2011). In this model, each in-

dividual can be in one of the following four states,

susceptible (S), exposed (E), infectious (I), and re-

covered (R). There are two main parameters in the

disease transmission model: contact probability and

transmission probability. Contact probability repre-

sents the chance of an effective contact between two

individuals in the same mixing group. Individuals in

the same age group have the same contact probability

in any given mixing group. The transmission proba-

bility P

trans

is the chance that an effective contact re-

sults in an infection. When a susceptible individual

having an effective contact with an infectious individ-

ual, the susceptible individual becomes exposed with

the probability P

trans

. An exposed individual will later

become infectious and then get recovered according

to the embedded disease natural history.

Changing of Spreading Dynamics for Infectious Diseases in an Aging Society: A Simulation Case Study on Flu Pandemic

455

3.2.5 Disease Natural History Model

The model of ﬂu’s natural history in (Germann et al.,

2006) is used is this system. Latent period refers to

the time between E and I, the individual does not

have any symptoms or signs of infection in this pe-

riod, while the incubation period is the time between

infection and symptom onset (Park and Ryu, 2018).

The time from I to R is called infectious period, in

which the infected individual can infect others. In this

model, the average latent period, incubation period

and infectious period are 1.2 days, 1.9 days and 4.1

days respectively, and there are one-third of asymp-

tomatic infectious individual.

3.3 Experiment Design

In this paper, there are a total of twelve experiments

consisting of six different P

trans

from 0.08 to 0.14

and two different mock populations. All others set-

ting besides P

trans

and mock population are ﬁxed. We

note that P

trans

of a typical seasonal ﬂu is about 0.08

(Fraser et al., 2009; Tsai et al., 2010).

The seeding policy is one index case that ran-

domly picked from the susceptible individuals every

ﬁve days (Tsai et al., 2010). The duration of a simula-

tion run is set to be 930 days. No intervention strategy

such as vaccination, school closure or social distanc-

ing policy is involved. We perform 100 runs for each

experiment then we take the average.

The mock population is then generated randomly

according to the household structure and the popula-

tion of all age groups. We then dump the age distri-

bution of the generated mock population and check

the actual census data from year-2000 and year-2010.

They are highly matched with both correlation coefﬁ-

cients being greater than 0.99 which is shown in Fig-

ure 2.

The basic reproductive number R

is deﬁned as

the expected number of new infections caused by a

typical infected individual in a susceptible population

(Heesterbeek, 2002; Heffernan et al., 2005). We can

determine whether an infectious disease will be a pan-

demic through R

. Usually, when R

is more than 1,

then it is called a pandemic. R

of twelve experiments

mention above are also run by the simulation system

in “R

mode”. When running in “R

mode”, the sys-

tem generated the same simulation world (included

mock population, mixing groups, ﬂows, agent’s be-

havior and disease transmission model) as “normal

mode”. The only different part is the seeding and the

trans

of non-seeded index cases. In “R

mode”, the

system will only seed one agent in each run. P

trans

of all non-seeded index cases (cases that infected by

Figure 2: Comparing generated mock population and the

actual census data.

the seeded case) is set become 0 to avoid interference.

When the seeded case recovered from infectious state,

this run of simulation ended and the infected case

number beside the seeded case will be recorded, then

went to the next run. We carry out 10,000 simulation

run and then take the average as the result of R

The average R

of each experiment is calculated

and summarized in Table 2. We chose those P

trans

’s

for experiments because the calculation result of R

is similar to the H1N1 pandemic in year 2009 (Fraser

et al., 2009). We note that with the same P

trans

, year-

2000 always have a larger value compared to that

of year-2010. The impact of the household struc-

ture mention in (Chang et al., 2015) may be a reason

because the average household size of year-2010 is

smaller than that of year-2000.

Table 2: Relations between P

trans

and R

trans

2000 2010

0.08 1.121 1.053

0.09 1.251 1.166

0.10 1.374 1.303

0.11 1.504 1.421

0.12 1.647 1.539

0.13 1.771 1.650

0.14 1.902 1.795

4 RESULTS

One of the advantages of using an agent-based simu-

lation is that we can get a ﬁner resolution during the

entire pandemic process, e.g., daily infected cases,

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

456

peak day, peak value and the infected cases in each

age group.

As shown in Figure 3, the number of total in-

fected cases in both years becomes higher as P

trans

goes higher, and year-2000 has a larger number com-

paring to that of year-2010, but the difference gets

smaller when P

trans

increases. This phenomenon is

due to the amount of susceptible individuals is ﬁxed,

it is harder to ﬁnd a susceptible individual when most

of the population are already in the R state when the

pandemic is almost end.

Figure 3: The total number of infected cases against differ-

ent transmission probabilities (P

trans

Figure 4 and Figure 5 show the peak day and peak

value during a pandemic. The peak day of year-2010

is a bit late comparing to year-2000 when P

trans

lower than 0.12. There is no signiﬁcant difference

when P

trans

gets higher. The peak number of daily

new cases of year-2000 society is higher than that of

year-2010.

Figure 4: Peak date of daily newly infected cases.

Figure 5: Peak value of daily newly infected cases.

5 DISCUSSION

We note the following interesting points for discus-

sion. The hospitalization rates of different age groups

are very different. Elders are likely to have a higher

hospitalization rate compared to others. Table 3

shows the hospitalization rates reported by (Meltzer

et al., 1999). We use those data to do a post-process

calculation and ﬁnd some interesting results.

Table 3: Hospitalization and Death Rates.

Variable Rates per 1,000 cases

0-19 20-64 65+

years old years old years old

Hospitalizations 1.22 7.88 28.83

Deaths 0.87 2.11 12.56

We show the total number of hospitalizations in

Figure 6, and hospitalizations separated by age groups

in Figure 7. In Figure 6, there is an intersection near

the point when P

trans

is 0.10. We can clearly see that

this intersection is mainly caused by the chaning of

the number of infected adults and elders in Figure 7.

Recall that the total infected cases in the year-2000

society is always higher than that of in the year-2010

society using all combinations of parameters. Due

to the differences in hospitalization rates for different

age groups, it causes the number of hospitalizations

of the year-2010 society to overtake the year-2000 so-

ciety.

We further show the number of deaths in Figure 8

and deaths separated by age groups in Figure 9. The

intersection moved a bit forward comparing to the to-

tal hospitalizations.

Figure 10 shows the daily new cases and hospi-

talizations when P

trans

is 0.08. We observe that the

pandemic in year-2000 is faster and the peak is higher

Changing of Spreading Dynamics for Infectious Diseases in an Aging Society: A Simulation Case Study on Flu Pandemic

457

Figure 6: The number of hospitalizations.

Figure 7: The number of hospitalizations by age groups.

Figure 8: The number of deaths.

Figure 9: The number of deaths by age groups.

compare to year-2010 in terms of daily new cases, but

the peak number of hospitalizations is about the same

due to having a higher hospitalization rate for the el-

ders.

Figure 10: The numbers infected cases and hospitalizations

trans

=0.080).

Figure 11: The numbers of infected case by age groups

trans

=0.080, year-2000).

SIMULTECH 2021 - 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

458

As observed from Figure 11, there are two peaks

during a pandemic. This phenomenon may be due to

the holiday’s effect during the summer vacation. We

note that the number of infected school-age children

signiﬁcantly drops during the summer vacation and

rises quickly when the holiday ends.

6 CONCLUSIONS AND FUTURE

WORK

We have reported our simulation results on the chang-

ing of spreading patterns in facing a ﬂu pandemic be-

tween the year 2000 and the year 2010 in Taiwan. In

the 10-year time-lag, Taiwan has shown great signs of

aging. The average population age is up 14% from

33.0 to 37.6 while the average household size is down

8% from 3.19 to 2.94. In facing a ﬂu pandemic, year-

2010 has less total infected cases and later peak date

comparing to year-2000 though the total population

is up 4% from 22.27 million to 23.16 million. How-

ever, due to the fact having more higher risk popula-

tion, e.g., people over the age of 65, higher demands

of hospital beds and a larger death toll are observed

(Meltzer et al., 1999). Though Census 2020 data has

yet to be released, the current preliminary data (Dept.

of Household Registration, Ministry of the Interior,

ROC (Taiwan), ) show the tend of aging to get worse,

namely the average population age is further 11% up

to 41.86 while the household size is plunged another

9% to 2.67. What are seen in this study will get worse.

We hope to motivate some further studies in redesign-

ing public health policies to better taking care of this

trend.

We remark that the approach we used in this pa-

per is useful for studying how disease spreads in Tai-

wan, but it has some limitation. First it is impossible

to simulate every possible spreading ways in the real

world though the validation of this simulation system

on a ﬂu model had done by (Tsai et al., 2010). Sec-

ondly, we only focus on the trend but not the exact

number when we interpret the results.

For future studies, we hope to rerun our experi-

ments when the year 2020 Census data are released.

We also want to study efﬁcacy of different interven-

tion mechanisms, such as mask wearing and vaccine

strategies, in an aging society. Public health policies

designed 20 years ago may not be as effective if used

now.

ACKNOWLEDGEMENTS

We thank Center for Survey Research (SRDA),

RCHSS, Academia Sinica, Taiwan for providing

data of Taiwan Census 2000 and 2010. This

study was supported in part by MOST, Taiwan

Grants 107-2221-E-001-017-MY2, 108-2221-E-001-

011-MY3 and 109-2327-B-010-005, and by Research

Center for Epidemic Prevention - National Yang Ming

Chiao Tung University (RCEP-NYCU).

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