Assess transmissibility of different influenza subtypes: Based on a SEIABR model

doi:10.21203/rs.3.rs-470103/v1

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Assess transmissibility of different influenza subtypes: Based on a SEIABR model

https://doi.org/10.21203/rs.3.rs-470103/v1

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Background: Influenza is a worldwide public health problem which causes a serious economic and health burden. In order to provide a scientific basis for improving the prevention and control level of influenza, using dynamic model to evaluate the infection rates of influenza different subtypes from 2010 to 2019 in China.

Methods: This article established SEIABR model and calculated the infection rates of different influenza subtypes by using the Berkeley Madonna software.

Results: The average infection rate of influenza was (7.95±1.27)×10^-10 , and influenza A was (7.25±0.82) ×10^-10, influenza B was (5.88±0.97)×10^-10. In addition, the infection rates of A /H1N1, A/H3N2, B/Yamagata and B/Victoria were (7.25±0.82) ×10^-10, (6.13±0.35) ×10^-10, (6.01±0.52) ×10^-10, (6.37±0.79) ×10^-10.

Conclusion: Between each year, flu transmission capacity had fluctuation. Influenza A was more transmissible than influenza B, and during the major subtypes, influenza A/H1N1 was the most transmissible.

Infectious Diseases

Influenza

SEIABR model

Transmission capacity

Influenza, as an acute respiratory infection caused by influenza virus, is transmitted through coughing, sneezing or touching surfaces, and then touching the mouth or eyes. Influenza is usually divided into four types: A, B, C, D, main influenza type A virus subtypes are H1N1, H3N2 and in B are Victoria and Yamagata [1]. Influenza viruses often mutate, with epidemiologically important antigenic variants appearing every two to three years under the immune pressure of the population. Because of the high flu virus mutation frequency, the public often lack immunity. And with the short incubation period, infectivity and transmission speed, influenza could suddenly outbreak, trigger a worldwide pandemic or local popular [2]. Go back in history, the flu pandemic in 1918 was the worst, infecting 500 million people worldwide and killing 40 million at least [3]. According to WHO (World Health Organization), every year in the World, 5-10% of adults and 20-30% of children are infected with influenza virus, resulting in 3-5 million severe cases and 290-650,000 deaths [4]. And the outbreak of influenza led to school suspension, business production, increasing number of hospital patients significantly and other phenomena. In 2019, the United States reported that there were at least 36 million cases of influenza, of which 370,000 were hospitalized and 22,000 died [5]. In China, since 2017, the incidence and severity of influenza have been on the rise. And the number of influenza outbreaks was also higher than the same period in previous years [6]. Influenza has become one of the most important public health issues in the world, all countries faced new challenges to prevent and control work particularly through COVID-19 and influenza global pandemic.

Timely surveillance, analysis, understanding of influenza flow characteristics and transmission capacity are important ways to prevent and control influenza outbreaks and pandemics. In recent years, mathematical model has become the mainstream of infectious disease research. Infectious disease dynamics model is a new method in epidemiological studies, mainly according to the law of population growth, study occurrence, development and dissemination to reflect disease characteristics, mechanism and ability. However, in influenza research field, most of dynamic models were limited to research a single outbreak, zone, subtype and prevention, not integrally considered transmission capacity of different subtypes. In addition, viruses mutated constantly, prevention and control measures to continuously upgrade, it is necessary to build a new model to fit recent influenza data again. Therefore, this paper simulated the infectivity of the main infection subtypes of influenza based on the SEIABR model, to provide a scientific basis for the prevention and control of different influenza subtypes.

Data source

The reported case of influenza from 2010 to 2019 in China were collected from China National Influenza Center(http://www.chinaivdc.cn/cnic). The demographic data came from National Bureau of Statistics of China(http://www.stats.gov.cn).

Models and statistical analysis

SEIABR model

Currently, influenza surveillance system did not cover all the cases in China, some flu patients did not diagnosis in hospital, and because of limited grassroots medical conditions, not all patients had etiological detection. Previous model did not consider the suffering from the flu but did not go to the sentinel hospital patients. In this study, a SEIABR model was developed to simulate the transmission of influenza in China. The human populations were subdivided into six classes, namely Susceptible(S), Exposed(E), Infected (I), Asymptomatic (A), Recovered(R), Untreated Patient(B) (Figure 1).

The model was established based on the following assumptions:1) A patient effective contacted with a susceptible person would transmit flu to a susceptible person, and the infected rate was β; 2) After infected, the exposed person (E) would turn to I, A or B, after an incubation period (1/ω), the number of newly I, A and B per unit time were wE. 3) c meant fatality rate, the fatality of I per unit time was (m+c)I. 4)γrepresented recovery rate, the number of R at time t was (γA+γB+γI). 5) Consider the natural birth and death of populations, set birth rate as μ, and mortality as m.

The differential equation based on SEIABR model was as follows, we set dS/dt, dE/dt, dI/dt, dA/dt , dB/dt and dR/dt to describe the number of population at time t :

Parameter estimation

In this study, there were eight parameters, which were infection rate (β), birth rate (μ), mortality(m), the proportion of asymptomatic infection rate of people (p), consultation rate (q) latency coefficient (w), case fatality rate (c) and removal rate of I (γ), all parameters and their sources were listed in Table 1. Through 1stopt, Matlab7.1 and Berkeley Madonna8.3.18, the residual square and least square method were used to estimate the influenza infection rate (β). β represented the probability of infection after a contact between an infected person and a susceptible person, it was also measuring the ability of virus transmission.

All parameters and initial values of each categories were list in Table 2.

Birth rate, mortality and Total population came from China Statistical Yearbook.
Inapparent infection rate and case fatality rate on the basis of researches ^[7-10] were 0.33,1%-0.5%.
Consultation rate according to the data from National Influenza Center and result of some Literatures ^[7-10]set as 25-0.70.
According to studies ^[7-10] and data fitting, we supposed A, B and I had the same recovery rate, so we set recovery time as 3-10 days, and the recovery rata(γ) is 1/10-1/3.

Influenza epidemics from 2010 to 2019

From January 1, 2010 to December 31, 2019, 671,693 cases of Influenza were reported. The average incidence was 4.90/10000, the lowest was 1.60/10000 in 2011, and the highest was 8.56/10000. There were 449,042 cases of influenza A, accounting for 66.85%, and 222,651 cases of influenza B, accounting for 33.15%. In influenza A, H3N2 accounted for 38.79% of the reported cases, followed by H1N1, accounting for 27.01%. Part of influenza B was not classified, and the proportion of Victoria subtype (10.71%) and Yamagata subtype (10.46%) was basically equal. Detail shown in Table 3.

The data showed that onset of influenza was cyclical in every year (Figure 2). In 2011, 2013, 2016, 2018 and 2019, there was only one influenza pandemic cycle in winter spring season. While, in 2010, 2012, 2014, 2015 and 2017, there were two cycles in winter spring season and summer fall season. Influenza A had peak period each year in winter spring season except 2012. H1N1 generally peaked at the beginning of the year, while H3N2 peaked at the middle or end of the year. Influenza B had a distinct epidemic cycle in 2010, 2012, 2016, late 2017 and early 2018.

Influenza transmission capacity assessment

Based on SEIABR model, the annual influenza infection rate (β) was simulated, the range of β is (6.02~9.44) ×10^-10，and average was (7.95±1.27) ×10^-10. β fluctuated to a certain extent among different years, from 2010 to 2013, the probability of influenza transmission was relatively high; after decreasing in 2014, it remained stable, and after 2017, it showed an upward trend. The result was shown in Table 4.

Comparison of the Different subtypes infection rates (β) of influenza A and B

Fit with actual data by Berkeley Madonna, the average infection rate of influenza A was (7.89±0.78)×10^-10，and influenza B was (5.88±0.97)×10^-10，Influenza A was more transmissible than influenza B. Using the same method to fit the infection rates of different subtypes of influenza. The results showed that the average infection rates of H1N1, H3, Yamagata and Victoria were (7.25±0.82)×10^-10, (6.13±0.35)×10^-10, (6.01±0.52)×10^-10, and (6.37±0.79)×10^-10. Influenza H1N1 had a higher prevalence rate than other influenza types. The detail data were shown in Table 5.

Because of the flexibility and unique advantages, dynamic model had become the mainstream mathematical model of infectious disease research [11]. This article, based on SEIABR model, simulated the occurrence of influenza in China from 2010 to 2019, and compared the transmission capacity of influenza different subtypes. The average β was (7.95±1.27) ×10^-10，which meant a patient contacted 10 billion person could lead to 6-9 infections. Taking China's 1.4 billion population as an example, one patient could lead to (0.94-1.29) susceptible people becoming infected. It was similar to TRACHT S M’s study in the community level [12], but lower than the transmission capacity of influenza outbreak studied by Tianmu Chen et al [13].

This study calculated and compared the probabilities of annual transmission of influenza A and influenza B, and found that between 2010 and 2019, the ability of influenza A to spread was higher than that of influenza B. This meant that a person infected with influenza A had a higher ability to infect vulnerable people than a person who infected with influenza B. Influenza A was the only influenza virus subtype had an animal host [14], its infectivity was manifested by the ability of horizontal gene transfer, which could cause repeated infection of the host [15]. Which may lead to the outbreak of an influenza A virus pandemic. The inherent characteristics of replicase of influenza B virus leaded to slower antigenic characteristics and slower gene evolution [16]. And Influenza B virus didn’t have animal host and pandemic potential [17]. Even so, the study found that the transmission ability of influenza B had an upward trend in recent years, which may be related to the antigen drift and antigen transfer of influenza B and how it escaped from the body's immune defense [18,19]. What was more, the Victoria strain in type B was prone to cluster infection [20], people should pay more attention to that.

Then, we compared the transmissibility of several common influenza subtypes. Among them, H1H1 had the strongest transmission capability, and the ability of other influenza subtypes was similar. H1N1 was a new influenza subtype in 2009, which contained the RNA gene fragments of avian influenza, swine influenza and human influenza viruses, and had the characteristics of both Asian swine influenza and African swine influenza viruses. Its strong transmission ability may be one of the main reasons for its worldwide pandemic [21,22]. And H1N1 was prone to mutated strains with an interval of 2 to 3 years. The change of antigen would reduce the protection efficiency of the vaccine, and it was difficult to take effective prevention and control measures in advance [23,24]. Beyond that, H1N1 was more likely to cause pneumonia than H3N1, resulting in a greater disease burden, which required more attention [25]. We also found that the total transmissible ability of influenza A was higher than that of the two subtypes (H1N1 & H3N2), which may be related to the superimposed epidemics of influenza A and H3N2 in winter and summer. And a phenomenon of co-infection among various subtypes of influenza A may enhance its transmission power [26].

The dynamics model of infectious diseases had better flexibility and could be adjusted according to the actual situation, so that the model was better consistent with reality. However, model was sensitive to the setting of the initial value, which was greatly influenced by subjective factors and empirical factors. Therefore, the setting of the initial value need to be carried out on reading large number of literatures and combining with the actual situation of influenza prevention and control in China.

Based on the SEIABR model, the probability β of influenza infection was calculated to be (7.95±1.27) ×10^-10, with a certain fluctuation among different years. Influenza A was more transmissible than influenza B, and of the major subtypes, influenza A (H1N1) was the most transmissible.

Ethics approval and consent to participate

Not applicable

Consent for publication

Not applicable

Availability of data and materials

In this study, all data were availability.

The reported case of influenza from 2010 to 2019 in China were collected from China National Influenza Center(http://www.chinaivdc.cn/cnic). The demographic data comes from National Bureau of Statistics of China(http://www.stats.gov.cn).

Competing interests

The authors declare that they have no competing interests.

Funding

The work was supported by the Natural Science Foundation of Hunan Province, China (No. 2020JJ4059), Changsha Science and technology Funds(kq2001025, kq1907130), Hunan Province Education Department [2018] No.505(JG2018B041), Hunan Province Major scientific and technological innovation projects(2020SK1015), Project of Hunan social science achievement appraisal committee(XSP21YBC338), Hunan Normal University Medical science -- interdisciplinary research project of humanities and social sciences.

The funders had in our study were the correspondence author (Yuan LV, Wenting Zha) and Meifang Quan.

Authors' contributions

H D, N Z and W Z mainly responsible for analysis data, building model;

H D and W Z mainly draft article and check English writing；

X R, M X, G L mainly in charge of the collection of data and searching for relevant parameters;

X H in charge of checking the article;

Y L, WZ and M Q mainly responsible for sponsorship of funds and final check the article.

All authors read and approved the final manuscript.

Acknowledgements

We sincerely appreciate everyone who helped us to complete this study.

[1]Daru Ye, Wen Zhou , Yong Feng , et al. Epidemic characteristics of influenza in Beihai People's Hospital from 2016 to 2019. Hainan Medical J ournal, 2021,32(03):393-397.

[2]Kim, Hyunsuh et al. “Influenza Virus: Dealing with a Drifting and Shifting Pathogen.” Viral immunology vol. 31,2 (2018): 174-183. doi:10.1089/vim.2017.0141

[3]Oxford J S . Influenza A pandemics of the 20th century with special reference to 1918: virology, pathology and epidemiology[J]. Reviews in Medical Virology, 2000, 10(2).

[4]Jiandong Zheng, Muli Zhang,Zhibing Peng, et al.Analysis of reported confirmed notifiable influenza cases and deaths in China, 2014-2018[J].Int J Virol,2020(01):6-7-8-9-10.

[5] Huang X, Zheng M, Wang P, Mok BW, Liu S, Lau SY, Chen P, Liu YC, Liu H, Chen Y, Song W, Yuen KY, Chen H. An NS-segment exonic splicing enhancer regulates influenza A virus replication in mammalian cells. Nat Commun. 2017 Mar 21; 8: 14751.

[6] Yan Lin, He Yu, Jian Li. Characteristics and TCM prevention and treatment of influenza in 2018[J]. Chinese Journal for Clinicians,2018,46(3):260-261.

[7]Dan Wang. Dynamical Study on several classes of influenza models. Beijing University of Civil Engineering and Architecture, 2017.

[8]Rongjie Wu. Data Simulation and Dynamic Analysis of the Influenza Model. Central China Normal University, 2013.

[9]Tianmu Chen. Dynamic model on strategies for containing influenza A(H1N1) pandemic in Changsha. Central South University, 2013.

[10]Yuanxiu Huang.Dynamic model on strategies for containing influenza outbreaks in schools [D]. Central South University, 2014.

[11]Zhien Ma, Yicang Zhou, Wendi Wang, et al. Mathematical modeling and study of infectious disease dynamics [M].Beijing: Science Press,2001.

[12] TRACHT S M, DEL VALLE S Y, HYMAN J M. Mathematical modeling of the effectiveness of facemasks in reducing the spread of novel influenza A (H1N1). PLoS ONE, 2010, 5(2): e9018.

[13]Tianmu Chen, Shuilian Chen, Zhi Xie, et al. Simulated effectiveness of control countermeasures for influenza outbreaks based on different asymptomatic infections and transmissibility.China Tropical Medicine,2017,17(5):470-475.

[14] Russell CA, Kasson PM, Donis RO, et al. Improving pandemic influenza risk

assessment. Elife, 2014,3:e03883.

[15]Petrova VN 1, Russell C. The evolution of seasonal influenza viruses. Nat Rev Microbiol, 2018,16(1):47-60.

[16]Yu H , Alonso WJ, Feng L, et al. Characterization of regional influenza seasonality patterns in China and implications for vaccination strategies: spatio-temporal modeling of surveillance data [J]. PLo S Med, 2013,10(11):e1001552.

[17]Ji-Rong Yang, Chuan-Yi Kuo, Hsiang-Yi Huang, et al. Seasonal dynamics of influenza viruses and age distribution of infected individuals across nine seasons covering 2009-2018 in Taiwan. J Formos Med Assoc, 2019,11. pii: S0929-6646(19)30448-6.

[18]Hongjie Yu, Wladimir J Alonso, Luzhao Feng, et al. Characterization of Regional Influenza Seasonality Patterns in China and Implications for Vaccination Strategies: Spatio-Temporal Modeling of Surveillance Data. PLo S Med, 2013, 10 (11):e1001552.

[19] Petrova VN, Russell CA. The evolution of seasonal influenza viruses [J]. Nat Rev Microbiol, 2018, 16(1):47-60.

[20]Muliu Liu, Jing Wang, Xuhui Yang, et al.Epidemiological characteristics of influenza clusters in Hangzhou.Preventive Medicine,2021,33(01):16-20.

[21]Yan Han, Nan Sun, Qiu-yue Lv, et al. Molecular epidemiology and phylogenetic analysis of HA gene of influenza A(H1N1)pdm09 strain during 2010-2014 in Dalian,

North China.Virus Genes, 2016,52(5):606-12.

[22]Shi W, Ke C, Fang S, et al. Co-circulation and persistence of multiple A/H3N2 influenza variants in China. Emerg Microbes Infect, 2019;8(1):1157-1167.

[23]Nihong Lu, Honglu Liu, Guozhong Li, et al.Clinical characteristics and prognosis of 42 patients with H1N1.Medicine and Pharmacy of Yunnan,2019,40(05):442-445.

[24]Jing Yang, Li Shen, Jin Liu, et al.Genetic evolutional analysis of the hemagglutinin and neuraminidase genes of influenza A H3N2 viruses in Zhenjiang city from 2014 to 2016 [J].Jiangsu Journal of Preventive Medicine,2021,32(01):8-12.

[25]Ziwei Wang, Lan Ma, Xiao Hong, et al.Study on the pathogenic characteristics of 106 children with influenza A.Beijing Medical Journal,2020,42(02):99-102.

[26]Szymański, K et al. “Infections with Influenza A/H3N2/ Subtype in Poland in the 2016/2017 Epidemic Season.” Advances in experimental medicine and biology vol. 1108 (2018): 93-98. doi:10.1007/5584_2018_244

Table 1 SEIABR Model parameters and definitions

Parameters	Definition	Source
S	Susceptible	N-E-I-A-B-R
E	Exposed	Calculated by differential equations
I	Infected	Actual outbreak data
A	Asymptomatic	Actual outbreak data
B	Untreated Patient	Actual outbreak data & Calculation
R	Recovered	The initial value R = 0
N	Population	China Statistical Yearbook
μ	Birth rate	China Statistical Yearbook
m	Mortality	China Statistical Yearbook
β	Infection rate	parameter estimation(OLS)
p	Inapparent infection rate	Literatures ^[7-10]
q	Consultation rate	National Influenza Center & Literatures ^[7-10]
w	Incubation relative rate	Literatures ^[7-10]
c	Case fatality rate	Literatures ^[7-10]
γ	Removal rate	Literatures ^[7-10]& Data fitting

Table 2 The original parameters of SEIABR model

Year	Parameters	Value (×10⁴)	Parameters	Value	Parameters	Value
2010	N	134091	μ	1.19%	m	0.71%
2011	N	134735	μ	1.19%	m	0.71%
2012	N	135404	μ	1.21%	m	0.72%
2013	N	136272	μ	1.21%	m	0.72%
2014	N	136782	μ	1.24%	m	0.72%
2015	N	137462	μ	1.21%	m	0.71%
2016	N	138271	μ	1.30%	m	0.71%
2017	N	139008	μ	1.24%	m	0.71%
2018	N	139538	μ	1.09%	m	0.71%
2019	N	140005	μ	1.05%	m	0.71%
2010-2019	p	0.33
	q	0.25-0.70
	w	1/7-1
	c	0.1%-0.5%
	γ	1/10-1/3

Table 3 Description of different influenza subtypes in China from 2010 to 2019 N (%)

Year

Different subtypes of influenza

Influenza A

Influenza B

Total

H1N1

H3N2

Not subtyped

Total

Yamagata lineage

Victoria lineage

Not subtyped

Total

2010

6654

(15.06)

12188

(27.60)

(0.00)

3389

(7.67)

22233 (50.34)

1171

(2.65)

2598

(5.88)

18164

(41.13)

21933 (49.66)

44166

2011

10369

(48.19)

2339

(10.87)

(0.00)

812

(3.77)

13520 (62.84)

879

(4.09)

1348

(6.27)

5768

(26.81)

7995 (37.16)

21515

2012

352

(0.79)

20885

(47.07)

(0.01)

1430

(3.22)

22671 (51.09)

3569

(8.04)

8597

(19.38)

9534

(21.49)

21700 (48.91)

44371

2013

13786

(31.07)

13113

(39.74)

(0.00)

396

(1.20)

27295 (82.73)

1666

(5.05)

227

(0.69)

3804

(11.53)

5697 (17.27)

32992

2014

18691

(26.09)

32958

(46.00)

(0.00)

294

(0.41)

51943 (72.50)

7884

(11.00)

673

(0.94)

11141

(15.55)

19698 (27.50)

71641

2015

1938

(2.75)

47404

(67.51)

(0.00)

114

(0.16)

49456 (70.43)

16639

(23.70)

1058

(1.51)

3066

(4.37)

20763 (29.57)

70219

2016

21363

(24.37)

29502

(33.65)

(0.00)

286

(0.33)

51151 (58.34)

5121

(5.84)

20134

(22.97)

11266

(12.85)

36521 (41.66)

87672

2017

16995

(17.16)

58115

(58.68)

(0.00)

131

(0.13)

75241 (75.97)

14858

(15.00)

6703

(6.77)

2236

(2.26)

23797 (24.03)

99038

2018

40681

(50.66)

6356

(7.92)

(0.00)

(0.09)

47109 (58.67)

18097

(22.54)

2345

(2.92)

12745

(15.87)

33187 (41.33)

80296

2019

50620

(42.26)

37709

(31.48)

(0.00)

(0.08)

88423 (73.82)

360

(0.30)

28261

(23.59)

2739

(2.29)

31360 (26.18)

119783

Total

181448

(27.01)

260570

(38.79)

(0.00)

7018

(1.04)

449042 (66.85)

70244

(10.46)

71944

(10.71)

80463

(11.98)

222651 (33.15)

671693

Table 4 Influenza contagiousness (β) assessment

Year	β (×10^-10)	Growth Amount (×10^-10)		Development Speed (%)		Growth speed (%)
Year	β (×10^-10)	Accumulated	Year by Year	Fixed Base Relative	Link Relative	Fixed Base Relative	Link Relative
2010	8.17	-	-	100.00	100.00	-	-
2011	9.22	1.05	1.05	112.85	112.85	12.85	12.85
2012	8.85	0.68	-0.37	108.32	95.99	8.32	-4.01
2013	9.66	1.49	0.81	118.24	109.15	18.24	9.15
2014	6.87	-1.30	-2.79	84.09	71.12	-15.91	-28.88
2015	6.62	-1.55	-0.25	81.03	96.36	-18.97	-3.64
2016	7.05	-1.12	0.43	86.29	106.50	-13.71	6.50
2017	6.03	-2.14	-1.02	73.81	85.53	-26.19	14.47
2018	7.79	-0.38	1.76	95.35	129.19	-4.65	29.19
2019	9.25	1.08	1.46	113.22	118.74	13.22	18.74

Table 5 Different subtypes infection rates (β) of influenza A and B (×10^-10)

Year	Influenza A			Influenza B
Year	H1N1	H3N2	Total	Yamagata	Victoria	Total
2010	7.93	6.20	8.13	5.35	6.03	5.77
2011	8.50	6.70	9.77	6.80	6.40	6.23
2012	6.85	6.15	7.46	5.83	4.93	4.35
2013	6.62	6.18	7.86	5.97	6.60	5.70
2014	6.15	5.48	6.87	4.56	5.68	4.60
2015	6.90	6.07	7.64	5.90	5.77	5.19
2016	7.10	5.80	7.16	6.09	6.33	6.95
2017	6.60	6.06	7.79	6.58	6.57	7.40
2018	8.56	6.03	8.00	6.54	6.06	6.30
2019	7.27	6.60	8.20	6.48	6.48	6.30

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Assess transmissibility of different influenza subtypes: Based on a SEIABR model

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