Dynamical Analysis for the Control of COVID-19: A Modified SEIR
Model
Chenhao Zhang
Department of Optical Science and Engineering, Fudan University, Shanghai, 200433, China
Keywords: Coronavirus Disease 2019, SEIR Model, Disease Consciousness, Isolation and Treatment.
Abstract: Objective: The paper of this research is to establish a new infectious disease dynamics model, which can be
used to evaluate the epidemic situation of covid-19 in 2019, and to evaluate the epidemic situation of covid-
19 in Hubei Province based on the SEIR model. Methods: Considering that covid-19 patients with latent
period have strong infectious ability, and the epidemic prevention information of the media has a positive
impact on mass epidemic prevention, an optimized SEIR epidemic dynamics model considering latent period
transmission ability, tracking and isolation intervention measures and mass disease awareness was
established. Referring to the official epidemic data of Hubei Province from January 23 to February 24, 2020
as the initial value of the dynamic system, the paper analyzes the epidemic situation in Hubei Province based
on the modified SEIR model to evaluate the impact of various measures and policies on the epidemic
transmission trend. Results: The theoretical analysis of the model shows that measures such as quarantine and
medical tracking can effectively inhibit the large-scale spread of the epidemic; centralized reception, layered
treatment and other important measures have played a key role in the rapid decline of the peak number of
infected people. Improving personal prevention awareness can curb the increase of infected people. In
addition, the publicity of news media can greatly increase people's disease awareness, so as to control the
development trend of epidemic situation and effectively reduce the peak number of infected people.
Conclusion: the modified SEIR model can be used for theoretical analyzing of covid-19 transmission and help
the government to formulate epidemic prevention policies.
1 INTRODUCTION
In recent decades, many infectious diseases are
constantly erupting, such as Ebora, swine flu, and
Chaga virus. At the end of 2019, an infectious disease
called New Coronavirus pneumonia (COVID 19) was
first launched in the world. The virus was highly
infectious and no vaccine was available at that time.
The COVID-19 has been responded very quickly
by China's government. In Hubei Province, where the
epidemic first broke out, the first level response to
major public health emergencies has been launched
since January 24, 2020. In order to control the spread
of the epidemic, the government has adopted isolation
measures based on past experience, such as stopping
performances and other activities, closing cinemas,
KTVs, schools and some workplaces to reduce crowd
gathering. In addition, the government has also
introduced policies to restrict the movement of people
to prevent the large-scale spread of the virus from
person to person. Hubei Province has also
implemented strict medical follow-up isolation, such
as a 14 day isolation observation of the people who
have been in contact with the infected people.
From the experience of China and other countries
in dealing with the epidemic situation, it can be found
that isolation measures are a very effective and
feasible anti-epidemic policy which has become the
first choice of many countries in facing the epidemic
situation. However, in the early stage of the epidemic,
some scholars did not consider the isolation factor in
the research on the development trend of covid-19
epidemic through dynamic model. For example,
according to the estimate results of the number of
infections by Jonathan et al. (Jonathan, 2020) on
January 24, 2020, as of February 4, the number of
COVID-19 infection cases in Wuhan will reach
190,000, far exceeding the actual number of
infections.
Also, with the development of technology,
communication software and news media, people
have more and more ways to obtain disease
information, which is conducive to timely taking
Zhang, C.
Dynamical Analysis for the Control of COVID-19: A Modified SEIR Model.
DOI: 10.5220/0011731600003607
In Proceedings of the 1st International Conference on Public Management, Digital Economy and Internet Technology (ICPDI 2022), pages 131-136
ISBN: 978-989-758-620-0
Copyright
c
2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)
131
protective measures to reduce the occurrence of
diseases. Especially, how the behavior of people with
strong awareness of disease and the government
quarantine methods affect the spread of infectious
diseases is worthy of targeted research. Over the
years, many mathematical models have been proposed
to study the impact of disease awareness on infectious
diseases. These models can be divided into two
categories: Network model and mean field model
There are two ways about the influence of disease
awareness on infectious diseases: 1) The first way is
to reduce the contact infection rate and take preventive
measures. 2) The media area m of independent
storehouse is introduced to represent the change of
disease information
As for the second mode of influence, most of the
relevant studies did not consider the constant input
rate of media coverage. For example, The SIS model
established by Basir et al. (Basir, 2018) In 2018
studied the impact of disease awareness and time lag
on infectious disease control. In 2020, Kumar et al.
(Kumar, 2020) established a SVIR model based on an
independent rate equation, taking into account the
impact of vaccination coverage information. These
studies consider the second mode of disease
awareness, but the growth of media coverage is only
related to the infected people.
In addition, recent conditions have shown that
carriers of the virus in the incubation period have a
strong risk of virus transmission because they have not
yet shown symptoms. However, the dynamic model
of the epidemic spread established by researchers
previously ignored this risk. At the same time, in
previous studies, isolation and prevention have not
been considered as factors influencing the spread of
epidemics. Therefore, this paper studies the effect of
disease awareness, virus latency, and quarantine
measures on the dynamic model of infectious
diseases. Under the above assumptions, an infectious
disease model with certain rationality and research
value is established, which provides theoretical
support for the prevention and control of the current
COVID-19 and some other infectious diseases in the
future.
2 METHODS
2.1 Improvement of SEIR Model
In the traditional SEIR model, S stands for the
susceptible population, I stands for the infected
population, E stands for the exposed population and R
stands for the recovered population. The model also
assumes because the infected individual will produce
antibodies after recovery. However, considering the
quarantine measures, quarantine susceptible [ S
],
quarantine exposed [E
] and quarantine infected [I
]
are taken into consideration. When it comes to the
impact of the disease awareness, a new population
group which stands for the awared susceptible [S
]
should also be added into the model. So that it will be
possible to estimate the impacts of both the disease
awareness and the quarantine measures on the spread
of a certain epidemic. In view of the fact that the
isolated infected people will beput into quarantine
treatment as soon as possible, all these people will
become hospitalized patients in this model [ H ].
Therefore, in the revised model [ S ], [ I ] and [ E ]
respectively refer to the susceptible, infected and
exposed persons who escape from the isolation
measures. In this way, the improved SEIR model in
this paper can be represented by figure 1.
2.2 Establishment of New Model
[q] is defined as isolation proportion, [β] is defined as
infection probability, [c] is defined as contact rate, [ρ]
is defined as effective contact coefficient (1 for
reference), Therefore, [ ρc ] refers to the effective
contact rate. Then we can give out the transmissive
relationship between susceptible people and other
Figure 1: The improved SEIR model.
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groups of people:
• The conversion rate from susceptible
population to quarantine susceptible population
is ρcq(1 −β)
• The conversion rate of susceptible population
to isolated latent population is ρcqβ
• The conversion rate from susceptible
population to exposed population is ρcβ(1 − q)
The effective information density [M(t)] adopted
in the model is a time dependent function and includes
the following three terms:
• The input value of disease awareness [o], a
constant in the whole model which reprents the
publicity efforts of government officials and other
news media for epidemic prevention and control
• The generation rate of autonomous disease
awareness [η] , reporting how people’s disease
awareness develop naturely through the spread of
disease
• The disease awareness decay rate [ θ] ,
modeling how people’s disease awareness decay over
time
In this case the effective information density
[M(t)] can be written ito the following expression:
𝑑𝑀
𝑑𝑡
= 𝑜 + 𝜂𝐼 − 𝜃𝑀 (1)
At the same time, the influence of non quarantine
infected person and exposed person on the susceptible
population should be taken into consideration, and the
susceptible person whose quarantine has been
removed is changed into susceptible person again. In
addition, it is reasonable to assume that patients during
latent period has the same ability of infection as that
of patients with symptoms.
Therefore, the equation of the number of the
susceptible is:
𝑑𝑆
𝑑𝑡
= −
[
𝜌𝑐𝛽 + 𝜌𝑐𝑞
(
1 −𝛽
)
]
𝑆
(
𝐼 + 𝐸
)
+ 𝜆𝑆
−𝑀𝑆
+ 𝜔𝑆
(2)
In equation (2), λ stands for the quarantine
release rate. Since the quarantine time in China is 14
days, the value of λ can be taken as 1/14.
The equation of the number of the exposed is:
𝑑𝐸
𝑑𝑡
= 𝜌𝑐𝛽
(
1 −𝑞
)
𝑆
(
𝐼 + 𝐸
)
−𝜎𝐸 (3)
In equation (3), σ stands for the transformation
rate from exposed to infected. Since the average latent
period is about seven days according to the China
Health Inspection Commission,the value of σ can be
taken as 1/7.
The equation of the number of the infected is:
𝑑𝐼
𝑑𝑡
= 𝜎𝐸 −
(
𝛿
+ 𝛼 + 𝛾
)
𝐼 (4)
In equation (4), δ
, α, γ
respectively represent
the quarantine rate, the fatality rate and the recovery
rate of the infected.
The initial values of the dynamic system refer to
the official data (State Health Commission of the
people's Republic of China) of Hubei Province. The
specific parameters and their values are described in
Table 1.
Table 1: Parameters used in the system and their values.
p
aramete
r
descri
p
tion default value Reference
𝑞
isolation proportion
1×10
(Wang, 2020)
𝛽
infection probability
2.05 × 10
(Wang, 2020)
𝑐
contact rate
3
𝜌
effective contact coefficient
1
𝑜
disease awareness value
0.1
(Liu, 2018)
𝜂
autonomous disease awareness rate
0.01
(Gani, 2018)
𝜃
disease awareness decay rate
0.06
(Gani, 2018)
𝜆
quarantine release rate
1
14
𝜔
disease awareness loss rate
0.2
(Gani, 2018)
𝜎
transformation rate
1
7
𝛿
quarantine rate of the infected
0.13
(Wang, 2020)
𝛼
fatality rate
2.7 × 10
(Wang, 2020)
𝛾
recovery rate of the infected
0.007
(Wang, 2020)
Dynamical Analysis for the Control of COVID-19: A Modified SEIR Model
133
3 RESULTS
Based on the SEIR model, this paper makes a
retrospective study on the epidemic situation in Hubei
Province. Furthermore, the author analyzes the
development law of the epidemic under the impact of
different control measures as well as media publicity.
3.1 Estimation of The Impact
Quarantine on Epidemic Situation
In the numerical simulation analysis, it is assumed that
the initial contact rate under the current prevention
and control measures is 2. By increasing the exposure
rate to simulate the development trend of people
infected with covid-19 under the condition of
ineffective prevention and control measures, the effect
of different prevention and control measures can be
evaluated. Figure 2 shows the epidemic simulation
under higher exposure probability of susceptible
persons (the exposure rates under three kinds of poor
management and control are 3, 4 and 6 respectively).
The analysis found that strict prevention and control
measures can effectively contain the large-scale
spread of the epidemic. It is estimated that if the
government does not issue strict quarantine measures
on January 23, 2020, the number of infections in
Hubei Province may reach more than twice the actual
number of infections. In addition, if measures are not
taken to control the epidemic, the virus will spread
faster, which will cause greater loss of life and
property, and cause serious social panic. In particular,
in the extreme cases of ineffective prevention and
control (i.e. 2 and 3), the number of people infected
with the epidemic will drop very slowly after reaching
the peak, and the duration of the epidemic will be very
long.
Figure 2: Influence of different prevention and control
measures.
In this paper, the author simulated the effect of
tracking and isolation measures, that is, the decrease
of tracking and isolation ratio. As shown in the figure
3, the isolation ratio decreases to 0.9, 0.8 and 0.6 times
in case of lack of quarantine1, 2and 3. The peak
number of infected people and the rising rate largely
increased. Especially when the isolation rate was
taken as 0.6q, the peak number of the infected nearly
doubles. In the numerical simulation, the overall trend
of the epidemic development is basically consistent,
and the number of infected people drops to 0 in about
250 days, which means that the epidemic is basically
over. Therefore, strict medical tracking and isolation
is an effective means to control the development of the
epidemic.
Figure 3: Influence of different medical quarantine
measures.
With the increase of daily contact rate between
personnel, personal daily safety protection will be
particularly important. The effective contact rate is
c
‘
= ρc. Where c is the daily contact rate between
daily personnel, ρ is the effective contact coefficient.
Figure 4 reflects the impact of the reduction of
effective contact coefficient on the development of the
epidemic situation (assuming that the number of
infected people does not jump), and sets the contact
rate between personnel. When the effective contact
coefficient is 0.5, 0.25 and 0.1 respectively. Personal
daily protective measures will not only ensure
personal safety, but also play a vital role in curbing the
development of the epidemic. Strict daily safety
protection helps advance the peak time of infection
and reduce the peak number. Under strict personal
protection measures, the peak number of infected
people can be reduced by nearly 60%.
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134
Figure 4: Influence of different daily self-protection.
Figure 5: Influence of different epidemic related media publicity.
3.2 Estimation of The Impact of
Disease Awareness on Epidemic
Situation
The broadcast of epidemic situation by TV news
media is one of the most important ways to obtain
people's disease awareness. Figure 4 simulates the
impact of different input rates of disease awareness on
the spread of epidemic situation in the early stage of
the epidemic when the media reports the epidemic
related information to different degrees. As shown in
figure 5, when the disease awareness input rate
reaches 10 times, 20 times and 50 times of the initial
value respectively, the rising rate of the number of
infected people decreases rapidly, and the peak of
infection also decreases greatly, and the number of
infected people decreases rapidly after experiencing
the peak, and soon reaches the disease-free
equilibrium point. Especially when the input rate of
disease awareness is 50, the peak number of infected
people is only one third of the original, and nearly half
of the time earlier to reach the disease-free
equilibrium. It can be seen that information factors
have a great impact on the prevention and control of
the epidemic, and the improvement of people's disease
awareness can effectively curb the development of the
epidemic.
4 CONCLUSION
In summary, the research results of this article show
that: First of all, prevention and control isolation and
medical tracking isolation can effectively curb the
spread of covid-19. Secondly, important measures
such as centralized reception and graded treatment can
Dynamical Analysis for the Control of COVID-19: A Modified SEIR Model
135
enable the infected people to receive better treatment,
and make the number of infected people drop rapidly.
Third, self-protection measures, such as wearing a
mask and paying attention to personal hygiene, can
also effectively reduce the infection rate. Finally,
when the epidemic just broke out, spreading
knowledge about epidemic prevention through
channels such as TV and the Internet can increase
people's awareness of the disease and cultivate good
hygiene habits for the public, thereby reducing the
severity of the epidemic.
What is more, the results of the optimized SEIR
model in this paper are in good agreement with the
actual development trend of the epidemic situation in
Hubei Province, thus confirming that the model is
reliable in the analysis of infectious disease
transmission situation. Furthermore, the result of this
research can provide theoretical support for relavant
policy making in the future.
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