A study on the transmission dynamics of COVID - 19 considering the

2025-04-30 0 0 938.68KB 22 页 10玖币

侵权投诉

A study on the transmission dynamics of COVID-19 considering the

impact of asymptomatic infection

Zonghao Zhang, Xiaotong Huang, Kedeng Cheng, Chuanqing Xu, Songbai Guo, Xiaojing Wang

School of Science

Beijing University of Civil Engineering and Architecture

Beijing 102699, China

Abstract: The COVID-19 epidemic has been spreading around the world for nearly three years,

and asymptomatic infections have exacerbated the spread of the epidemic. To evaluate the role of

asymptomatic infections in the spread of the epidemic, we develop mathematical models to assess

the proportion of asymptomatic infections caused by different strains of the main covid-19 variants.

The analysis shows that when the control reproduction number is less than 1, the disease-free

equilibrium point of the model is globally asymptotically stable; and when the control reproduction

number is greater than 1, the endemic equilibrium point exists and is unique, and is locally

asymptotically stable. We fit the epidemic data in the four time periods corresponding to the selected

614G, Alpha, Delta and Omicron variants. The fitting results show that, from the comparison of the

four time periods, the proportion of asymptomatic persons among the infected persons gradually

increased. We also predict the peak time and peak value for the four time periods, and the results

indicate that the transmission speed and transmission intensity of the variant strains increased to

some extent. Finally, we discuss the impact of the detection ratio of symptomatic infections on the

spread of the epidemic. The results show that with the increase of the detection ratio, the cumulative

number of cases has dropped significantly, but the decline in the proportion of asymptomatic

infections is not obvious. Therefore, in view of the hidden transmission of asymptomatic infections,

the cooperation between various epidemic prevention and control policies is required to effectively

curb the spread of the epidemic.

Keywords: COVID-19; Asymptomatic infections; Control reproduction number; Lyapunov

function; Data Fitting.

Mathematics Subjects Classification 2010: 34A34, 92B05

1. Introduction

Since its outbreak at the end of 2019, COVID-19 has had a severe impact on countries around the

world. How to effectively control the spread of the epidemic and restore normal production and life

is still an issue that governments need to consider. To control the spread of COVID-19, many

measures have been taken, including non-pharmacological interventions, pharmacological

interventions, vaccinations, and more. However, due to the continuous emergence of variants, the

 Corresponding Author: xuchuanqing@bucea.edu.cn

epidemic prevention measures did not achieve the expected effect.

There are a large number of contagious asymptomatic infections during the spread of COVID-19

[1,2,3,4]. This feature determines the high concealment of the spread of COVID-19, and leads to

an increase in the difficulty of epidemic prevention and control. There have been a large number

of research results on asymptomatic infections of new coronary pneumonia, including age

distribution, average proportion, and transmission intensity [5,6,7]. In addition, some researchers

have studied the spread of COVID-19 by establishing dynamic models including asymptomatic

infections. Ruan et al. established a time-varying COVID-19 transmission compartment model

including asymptomatic infected persons, simulated and reviewed the development process of the

Wuhan epidemic, and obtained that the asymptomatic proportion of infected persons was about

20% [8]. Rahul Subramanian et al. established a COVID-19 transmission model including

asymptomatic infections, quantified asymptomatic infections in New York City, and obtained

asymptomatic infections accounted for about 60% [9]. Mohamed Amouch et al. proposed a new

epidemiological mathematical model of the spread of COVID-19 disease, fitted the outbreak in

Monaco, and obtained that the proportion of asymptomatic patients was 30% [10]. However, these

studies are all conducted for a specific variant, and cannot effectively reflect the changes caused

by variant iterations.

In the more than two years since the first appearance of COVID-19, many countries and regions

around the world have experienced repeated outbreaks. Taking England as an example, although

multiple rounds of lockdown measures have been adopted to control the spread of the epidemic,

such epidemic prevention measures have not been fully effective. When the epidemic prevention

measures were gradually lifted, the epidemic rebounded again. We believe that asymptomatic

infections have played a very important role in the rebound of the epidemic. The lockdown measures

have effectively reduced the number of infected people to a certain extent, but because large-scale

screening tests were not adopted, there were still a certain number of asymptomatic infections in the

population. After the epidemic prevention measures are lifted, these undetected asymptomatic

infections will cause the next round of outbreaks. If the number of asymptomatic infections can be

effectively estimated in the early stage of the next outbreak, and certain epidemic prevention and

control measures are taken, the spread of the epidemic can be delayed to a certain extent. We

establish an improved SEIAR infectious disease dynamics model to assess the role of asymptomatic

infections in the early stages of epidemic transmission.

The remainder of this article is organized as follows. In Section 2, we present the COVID-19

infectious disease model and analyze the stability of the equilibrium point. In the third section, we

use the established model to fit the actual epidemic data, and conduct a comparative analysis of the

relevant kinetic parameters. In the last section, we conclude and discuss.

2. Model establishment and analysis

2.1 Model establishment

There are two typical characteristics of the spread of COVID-19. First, there are a large number of

asymptomatic infected people with new coronary pneumonia. The second is that COVID-19 patients

have a longer exposure period and have differences in infectivity. Based on our knowledge of

COVID-19, we have the following assumptions in our model:

(A1) We divide the exposure period into two parts: the early stage and the later stage, in which the

early stage is not infectious and the later stage is infectious;

(A2) For symptomatic infections, we assume that symptomatic infections can be screened as long

as they are tested, and that the detected symptomatic infections are completely isolated and no longer

contagious;

(A3) Asymptomatic infections were assumed not to be tested, and deaths from illness in

asymptomatic infections were not considered.

Based on the above assumptions, we establish a COVID-19 transmission compartment model

including asymptomatic infected persons. The model divides the general population into susceptible

(

), pre-exposure patients ( 1

E), late-exposure patients ( 2

E), detected symptomatic infections ( 1

I),

undetected symptomatic infections ( 2

I), asymptomatic infections ( A) and recovered ( R). Its

dynamic flow chart is shown in Figure 1.

Fig.1 Flow chart of the COVID-19 transmission dynamics model containing seven

compartments. The compartments represented by the red box is infectious, and the compartments

represented by the blue box is not infectious.

The corresponding propagation dynamics equation is constructed as follows:

 

   

 

   

 

2 2

2 2 1

1 2

2 1 1 1

2 2 2 2

1 3

1 1 2 2 3

1 ,

dS S E I A S

S E I A E

dE E E

dI E I

dA E A

dR I I A R

  

    

  

   

    

  

   

     



     



  



   





    



  



   





(1)

The parameters in system (2.1) are explained as follows.



is the daily number of births and



is the daily natural mortality rate. The parameter



represents the basal transmission rate, and



represents the conversion rate from patients in the pre-exposure period to patients in the late-

exposure period.



represents the conversion rate from patients in the pre-exposure period to

asymptomatic infected persons, and



represents the conversion rate from patients in the late

exposure period to infected persons.



is the weight of the transmission intensity of the

asymptomatic infection relative to the symptomatic infection, and



is the rate of testing among

the symptomatic infection.

1 2 3

, ,

  

is the recovery rate of detected symptomatic infections,

undetected symptomatic infections, and asymptomatic infections, respectively.

1 2

 

is the

mortality rate of detected symptomatic infections and undetected symptomatic infections,

respectively.

2.2 Calculation of disease-free equilibrium point and controlled reproduction number

Obviously, there is always a disease-free equilibrium point

 

0 0

= , 0, 0, 0, 0, 0, 0

P S in system (1),

where 0



 

. Then we use the next generation matrix method to calculate the control

reproduction number of system (1). The Jacobian matrices

and

at the disease-free

equilibrium point are obtained from system (1) as

0 0 0

0 0

0 0 0 0 0

S S S

  

 

 



 

 

 

1 1

2 2

0 0 0 0

0 0 0

0 0 0 .

0 1 0 0

0 0 0

  

  

   

    

  

 

 

 

 

 

   

 

   

 

 

 

The control reproduction number is the spectral radius of the

FV 

, therefore we get

 

  

2 2 3

= .

  

 

           

 



 

 

      

 



2.3 Existence of the endemic equilibrium point

Theorem 2.3. When



, the system (1) has a unique positive equilibrium point

 

1 2 1 2

= , , , , , ,P S E E I I A R

       

Proof. Using the equilibrium equation of system (1) at the endemic equilibrium point, we can get

 

  

 

  

    

  

2 2 3

2 1 1 1

1 1

2 1 1

2 2 3

1 1

1 1 2 2 3

, ,

1, ,

E E I E

I E A E

  

 

 

        

 

      

   

      

   



            



   





 



  

 

    

 

 

   



 

   

 



  

 

      

 

(2)

Furthermore, according to the equilibrium equation, we obtain

 

S E

   

 

     

Simplify to get

   

1 1 0

C C

E E S

     

 

 

     

 

 

Therefore, we can get

E



 

 

   



 

   



文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

AstudyonthetransmissiondynamicsofCOVID-19consideringtheimpactofasymptomaticinfectionZonghaoZhang,XiaotongHuang,KedengCheng,ChuanqingXu,SongbaiGuo,XiaojingWangSchoolofScienceBeijingUniversityofCivilEngineeringandArchitectureBeijing102699,ChinaAbstract:TheCOVID-19epidemichasbeenspreadingaroundtheworl...

展开>> 收起<<

A study on the transmission dynamics of COVID - 19 considering the.pdf

共22页,预览5页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

A study on the transmission dynamics of COVID - 19 considering the

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: