Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T04:55:29.389Z Has data issue: false hasContentIssue false
  • English
  • Français

The transmissibility of hepatitis C virus: a modelling study in Xiamen City, China

Published online by Cambridge University Press:  25 November 2020

Yao Wang ,
Zeyu Zhao ,
Mingzhai Wang ,
Mikah Ngwanguong Hannah Open the ORCID record for Mikah Ngwanguong Hannah [Opens in a new window] ,
Qingqing Hu ,
Jia Rui ,
Xingchun Liu ,
Yuanzhao Zhu ,
Jingwen Xu  and
Meng Yang
...Show all authors
Yao Wang
Affiliation:
State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen361102, People's Republic of China
Zeyu Zhao
Affiliation:
State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen361102, People's Republic of China
Mingzhai Wang
Affiliation:
Xiamen Center for Disease Control and Prevention, Xiamen361021, People's Republic of China
Mikah Ngwanguong Hannah
Affiliation:
Medical College, Xiamen University, Xiamen City, Fujian Province, People's Republic of China
Qingqing Hu
Affiliation:
Division of Public Health, School of Medicine, University of Utah, 201 Presidents Circle, Salt Lake City, UT84112, USA
Jia Rui
Affiliation:
State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen361102, People's Republic of China
Xingchun Liu
Affiliation:
State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen361102, People's Republic of China
Yuanzhao Zhu
Affiliation:
State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen361102, People's Republic of China
Jingwen Xu
Affiliation:
State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen361102, People's Republic of China
Meng Yang
Affiliation:
State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen361102, People's Republic of China
Jing-An Cui
Affiliation:
Department of Mathematics, School of Science, Beijing University of Civil Engineering and Architecture, Beijing, People's Republic of China
Yanhua Su*
Affiliation:
State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen361102, People's Republic of China
Benhua Zhao*
Affiliation:
State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen361102, People's Republic of China
Tianmu Chen*
Affiliation:
State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics, School of Public Health, Xiamen University, Xiamen361102, People's Republic of China
*
Authors for correspondence: Yanhua Su, E-mail: [email protected]; Benhua Zhao, E-mail: [email protected]; Tianmu Chen, E-mail: [email protected]
Authors for correspondence: Yanhua Su, E-mail: [email protected]; Benhua Zhao, E-mail: [email protected]; Tianmu Chen, E-mail: [email protected]
Authors for correspondence: Yanhua Su, E-mail: [email protected]; Benhua Zhao, E-mail: [email protected]; Tianmu Chen, E-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

This study aimed at estimating the transmissibility of hepatitis C. The data for hepatitis C cases were collected in six districts in Xiamen City, China from 2004 to 2018. A population-mixed susceptible-infectious-chronic-recovered (SICR) model was used to fit the data and the parameters of the model were calculated. The basic reproduction number (R0) and the number of newly transmitted cases by a primary case per month (MNI) were adopted to quantitatively assess the transmissibility of hepatitis C virus (HCV). Eleven curve estimation models were employed to predict the trends of R0 and MNI in the city. The SICR model fits the reported HCV data well (P < 0.01). The median R0 of each district in Xiamen is 0.4059. R0 follows the cubic model curve, the compound curve and the power function curve. The median MNI of each district in Xiamen is 0.0020. MNI follows the cubic model curve, the compound curve and the power function curve. The transmissibility of HCV follows a decreasing trend, which reveals that under the current policy for prevention and control, there would be a high feasibility to eliminate the transmission of HCV in the city.

Keywords

Hepatitis Cmathematical modeltransmissibilitytrend
Type
Original Paper
Information
Epidemiology & Infection , Volume 148 , 2020 , e291
Check for updates
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

Introduction

Hepatitis C is an infectious disease caused by hepatitis C virus (HCV) infection [Reference Webster, Klenerman and Dusheiko1], which is the main cause of liver cirrhosis and hepatocellular carcinoma [Reference Shi2, Reference Taherkhani and Farshadpour3]. It has become a serious public health problem in the world because its susceptible populations are widely distributed, coupled with the fact that it has a poor prognosis. According to the WHO statistics, in 2017, there were about 150 million cases of chronic HCV infection, increasing at a rate of 3–4 million per year, and the number of deaths due to HCV infection reached 400 000 per year [Reference Jacobson4, 5]. In recent 10 years, the incidence of hepatitis C in China has been on the rise and has not been effectively controlled. There are still gaps in research on the transmissibility of hepatitis C. In China, HCV infection is mainly blood-borne [Reference Shi2]. Unsafe injections/blood transfusions and contaminated equipment used in medical-related procedures are the main causes of hepatitis C infection [Reference Mohsen6]. Currently, another major cause of hepatitis C transmission is injecting drugs. In the Eastern Mediterranean and European countries, cases of infection due to injection of drugs account for a large proportion of new infections [Reference Mohsen6–Reference Mitruka8]. HCV infection can be effectively controlled in the future if blood products can be strictly tested, blood transfusion agencies strictly regulated and injection safety controlled.

Currently, mathematical models are an effective method to evaluate the transmissibility of various infectious diseases, predict future morbidity and evaluate the effectiveness of prevention and treatment [Reference Cui9–Reference Breban16]. There are a few model studies on hepatitis C; curve regression model, SEACR dynamic model and multi-stage SEIR model, which are widely used [Reference Shi and Cui11, Reference Pan and Chakrabarty17–Reference Kitagawa19]. Our previous study explored the principle of a susceptible-infectious-chronic-recovered (SICR) model, and used the next-generation matrix approach to deduce the equation of the basic reproduction number (R 0) of hepatitis C [Reference Cui9]. However, the transmissibility of hepatitis C in a mixed population still remains unclear.

In this research, the SICR model of mixed population was used, and R 0 and the number of newly transmitted cases per month by a primary case (MNI) were applied as indicators to quantitatively estimate the transmissibility of HCV infectious individuals. The SICR model was established for hepatitis C cases in various districts of Xiamen from 2004 to 2018 to evaluate the reliability of the model and predict the transmissibility of hepatitis C.

Methods

Ethic statement

This effort of investigation was part of CDC's routine responsibility in Xiamen City. Therefore, institutional review and informed consent were waived by Medical Ethics Committee of Xiamen Center for Disease Control and Prevention on the following grounds: (1) all data were anonymised; (2) neither medical intervention nor biological samples were involved; (3) study procedures and results would not affect clinical management of patients in any form.

Data collection

During this study, the cases from 1 January 2004 to 31 December 2018 were collected from six areas (Huli District, Siming District, Jimei District, Xiang'an District, Haicang District and Tong'an District) in Xiamen City. For each case, the following information was obtained: age, sex, occupation, date of onset of disease, date of diagnosis, classification of cases (acute cases, chronic cases and unclassified cases), date of death, etc. Data on the incidence of hepatitis C were used to assess the local transmissibility of hepatitis C. The demographic data of Xiamen City came from the Statistical Yearbook of Xiamen City. This study collected monthly data on the mortality rate for chronic hepatitis C in China from January 2004 to December 2018, released by the national health commission of the People's Republic of China.

Transmission model

The SICR model was established based on the natural history of hepatitis C. Since re-infection of HCV is not included in the data reporting system in China, re-infection of HCV was not considered in this model. The model was based on the following assumptions:

  1. (1) The model divides the population into susceptible population (S), acute hepatitis C (I), chronic hepatitis C (C) and recovering population (R).

  2. (2) Acute cases of hepatitis C have the same infectious power as chronic cases of hepatitis C. The transmission rate of acute or chronic hepatitis C cases is denoted as β.

  3. (3) It is assumed that a part of acute cases (pγI) can be transformed into chronic hepatitis C cases, and the other parts ([1 − p]γI) cases will develop into R. The rate from I to C and R is proportional to the number of the corresponding population, and the proportionality coefficient is γ.

  4. (4) Considering the natural birth and death of the population, there is no vertical transmission of the disease, and newborns of all groups are susceptible. We assumed that the natural birth rate is a and the natural death rate is b.

Therefore, the flow chart of SICR model without intervention is as shown in Figure 1. The model is represented by the differential equations as follows:

$$\displaystyle{{{\rm d}s} \over {{\rm d}t}} = aN-\beta S\lpar I + C\rpar -bS$$
$$\displaystyle{{{\rm d}I} \over {{\rm d}t}} = \beta S\lpar I + C\rpar -\lpar b + \gamma \rpar I$$
$$\displaystyle{{{\rm d}C} \over {{\rm d}t}} = p\gamma I-\lpar \mu + b\rpar C$$
$$\displaystyle{{{\rm d}R} \over {{\rm d}t}} = \lpar 1-p\rpar \gamma I-bR$$
$$N = S + I + C + R$$

Fig. 1. Flow chart of SICR model.

The left-hand side of the equation represents the instantaneous rate of change of S, I, C and R at time t; whereas β, p, γ, a, b and μ respectively indicate the relative rate of transmission, the proportion of chronic cases, removal rate parameters for infected individuals, birth rate, natural death rate and case fatality rate.

Parameter estimation

The annual parameter β of each district, county and city was estimated by the model. Based on previous studies [Reference Hart and Ferguson18], the time for acute hepatitis C cases to develop into chronic hepatitis C cases is as long as 6 months, that is, the course of infectious hepatitis C disease is 1–6 months, and chronic hepatitis C cases will develop further on this basis. Therefore, the time limit between acute hepatitis C and chronic hepatitis C is generally 6 months, and this study used 6 months as the course of disease to simulate, so it follows that γ = 1/6, γ = 0. 1667. Parameters a and b were calculated from the collected demographic data. The parameters p and µ were calculated from the collected epidemiological data. Natural birth and death rates of the people of Xiamen were derived from the Xiamen statistical yearbook published by the Xiamen bureau of statistics (2004–2018).

Index of transmissibility

R 0 and MNI were used in this study to quantify the transmissibility of hepatitis C. The R 0 represents the number of new cases transmitted directly within the infectious period of a source of infection, and is a parameter used to determine whether the disease is prevalent. Based on our previous study [Reference Cui9], the equation of R 0 was shown as follows:

$$R_0 = \displaystyle{{\beta \alpha N} \over {b\lpar {b + \gamma } \rpar }} + \displaystyle{{\beta \alpha Npr} \over {b\lpar {\mu + b} \rpar \lpar {b + \gamma } \rpar }}$$

MNI is also used to quantitatively estimate the transmissibility of an infectious individual, and is represented by the following equation:

$$MNI = \beta \times S$$

Simulation and statistical analysis

Eleven models, linear regression (LIN), logarithmic curve (LOG), inverse function curve (INV), quadratic curve (QUA), cubic curve (CUB), composite curve (COM), power function curve (POW), S-shaped curve (S), growth curve (GRO), exponential curve (EXP) and logistic curve (LGS) models, were used in SPSS 21.0 to fit the curve of R 0 and MNI, and the optimal model of quantitative indicator MNI was determined by the size of R 2 and P value. Meanwhile, the 95% confidence interval (CI) of the R 0 and MNI curve was predicted for interval estimation.

The 11 curve models and equations are as follows (‘Y’ represents R 0 or MNI, ‘x’ represents the time (year)):

  • Linear regression (LIN): Y = b 0 + b 1x

  • Logarithmic curve (LOG): Y = b 0 + b 1ln(x)

  • Inverse function curve (INV): Y = b 0 + b 1/x

  • Quadratic curve (QUA): Y = b 0 + b 1x + b 2x 2

  • Cubic curve (CUB): Y = b 0 + b 1x + b 2x 2 + b 3x 3

  • Composite curve (COM): $Y = b_0 + b_1^x$

  • Power function curve (POW): $Y = b_0 + x^{b_1}$

  • S-shaped curve (S): $Y = {\rm e}^{\lpar b_0 + b_1/x\rpar }$

  • Growth curve (GRO): $Y = {\rm e}^{\lpar b_0 + b_1x\rpar }$

  • Logistic curve (LGS): $Y = 1/\lpar 1/\mu + b_0b_1^x \rpar$

  • Exponential curve (EXP): $Y = b_0{\rm e}^{b_1x}$

Berkeley Madonna 8.3.18 software was used for mathematical simulation. According to optimal parametric results of the software's calculation and output of the minimum root mean square, the hepatitis C epidemic curve was constructed. SPSS 21.0 curve fitting was used for goodness of fit test. R 2 and P values were used to compare the fitting degree between model fitting data and actual data, based on our previous study [Reference Zhang20].

Result

Epidemiological characteristics

From 2004 to 2018, 2888 HCV cases were reported in Xiamen City, including 224 acute cases (7.76%), 1524 chronic cases (52.77%) and 1140 non-classified cases (39.47%). The variation trend for incidence of various cases from 2004 to 2018 is shown below (Fig. 2).

Fig. 2. Annual trends of acute, chronic and unclassified morbidity.

There were 1703 male cases (59.0%) and 1185 (41.0%) female cases. The changes of hepatitis C incidence among different genders in Xiamen from 2004 to 2018 are as follows (Fig. 3).

Fig. 3. Incidence rates by gender for each year.

According to the statistics of the time of onset and diagnosis for a single case, the mean value of the interval between the onset and time of diagnosis for each case was calculated in months (Fig. 4). From 2004 to 2018, the interval between onset and diagnosis showed a general decreasing trend.

Fig. 4. Mean time interval between time of onset and diagnosis (in months).

The incidence of hepatitis C in all districts and counties (cities) of Xiamen City from 2004 to 2018 is described as follows (unit/1 million): the mean incidence of HCV was 52.95 (95% CI 42.86–63.04) in Huli district, 79.07 (95% CI 63.82–94.32) in Siming district, 44.42 (95% CI 31.56–57.28) in Jimei district, 50.48 (95% CI 29.61–71.34) in Xiang'an district, 63.38 (95% CI 45.45–81.31) in Haicang district and 35.77 (95% CI 27.62–43.91) in Tong'an district. Spatial coordinates of the incidence of hepatitis C in six districts of Xiamen from 2004 to 2018 (Fig. 5) show that the incidence of hepatitis C in all districts of Xiamen City was at a low level from 2004 to 2006. The incidence rates in Siming district and Huli district were the highest in Xiamen from 2005 to 2014, and the incidence rates in Siming district and Huli district were lowest among all districts of Xiamen from 2015 to 2018. Therefore, the incidence rates in Siming district and Huli district decreased rapidly after 2015. In general, the incidence of disease in all districts of Xiamen City after 2009 was significantly higher than that before 2009.

Fig. 5. Statistical chart of annual incidence of hepatitis C in various districts of Xiamen City.

Transmissibility of hepatitis C

The results of model fitting curve and actual case change curve shows that the fitting effect of the curve between the predicted number of chronic disease cases per month and the actual number of chronic disease cases per month in six districts of Xiamen City was statistically significant, with an R 2 range of 0.193–0.440, P < 0.01 (Fig. 6 and Table 1). From 2004 to 2018, R 0 values and MNI values in the six districts of Xiamen increased initially, and then decreased slowly (Fig. 7). The median value and threshold of R 0 in each district are described as follows: 1.07 (0.01–2.26) in Huli district, 1.43 (0.01–2.79) in Siming district, 0.04 (0.00–1.27) in Jimei district, 0.50 (0.00–2.15) in Xiang'an district, 0.38 (0.00–1.27) in Haicang district and 0.02 (0.00–0.81) in Tong'an district. The median MNI and threshold values in each district are described as follows (unit/10 thousandth): 31.75 (4.49–61.40) in Huli district, 46.61 (8.21–70.31) in Siming district, 17.27 (0.03–32.81) in Jimei district, 15.11 (1.23–28.34) in Xiang'an district, 17.15 (2.45–31.83) in Haicang district and 14.80 (1.92–103.15) in Tong'an district. From 2004 to 2018, the median, minimum and maximum variation curves of R 0 value and MNI value in all districts of Xiamen City are shown in Figures 8 and 9. According to the curve change of median R 0 value, it can be seen that it was at a low level before 2009, increased from 2009 to 2014 and decreased from 2014 to 2018. According to the change of MNI median value curve, it can be seen that it showed an upward trend from 2004 to 2012, and a downward trend from 2012 to 2018. The overall median values of R 0 and MNI from 2004 to 2018 were 0.4059 (0.0037–1.4262) and 0.0020 (0.0003–0.0040), respectively.

Fig. 6. Results of model fitting curve and actual case change curve.

Fig. 7. R 0 and MNI were used to represent the transmissibility of hepatitis C in six districts of Xiamen City. (a) The curve of the median of R 0; (b) the curve of the median of MNI.

Fig. 8. Variation trend of median, minimum and maximum value of R 0 in Xiamen.

Fig. 9. Variation trends of median, minimum and maximum of MNI values in Xiamen.

Table 1. Estimation of fitting degree curve between model and actual situation

The median curve of R 0 value was fitted with 11 curve models (Table 2). According to the fitting results and the reduction or growth pattern of the virus in the process of population transmission, the cubic model, the composite function model and the power function model were selected as the appropriate models, which fitted the confidence band of the predicted value (Fig. 10). ‘x’ represents the time (year). After selecting the appropriate model for curve fitting, the formula for the change of R 0 value with time can be calculated. The median value of R 0 from 2004 to 2018 was fitted to the cubic model curve ‘R 0 = 0.6414 − 0.5471x + 0.1058x 2 − 0.0046x 3’, the median value of R 0 from 2004 to 2018 was fitted to the Compound curve ‘R 0 = 0.0033 × 1.5788x’ and the median value of R 0 from 2004 to 2018 was fitted to the Power function curve ‘R 0 = 0.0010x 2.5959’.

Fig. 10. Trend of R 0 value of hepatitis C transmissibility fitting curve by time. (a) The cubic curve; (b) the compound curve and (c) the power function curve.

Table 2. Various curve fitting results of R 0 value

The median curve of MNI value was fitted with 11 curve models (Table 3). According to the fitting results and the reduction or growth pattern of the virus in the process of population transmission, the cubic model, the composite function model and the power function model were selected as the appropriate models, which fitted the confidence band of the predicted value (Fig. 11). ‘x’ represents the time (year). After selecting the appropriate model for curve fitting, the formula for the change of MNI value with time can be calculated. The median value of MNI from 2004 to 2018 was fitted to the Cubic model curve ‘MNI = 0.0003 − 7.8077 × 10−5x + 7.4274 × 10−5x 2 − 4.1024 × 10−6x 3’, the median value of MNI from 2004 to 2018 was fitted to the Compound curve ‘MNI = 0.0005 × 1.1487x’ and the median value of MNI from 2004 to 2018 was fitted to the Power function curve ‘MNI = 0.0003x 0.8876’.

Fig. 11. Trend of MNI value of hepatitis C transmissibility fitting curve by time. (a) The cubic curve; (b) the compound curve and (c) the power function curve.

Table 3. Results of various curve fittings of MNI values

Discussion

The dynamic transmission model of infectious diseases has been established to take corresponding measures to predict the epidemic trend of hepatitis C in the future [Reference Zheng21–Reference Hutchinson24]. In accordance with the WHO's goal of eliminating hepatitis C in 2030, this study, for the first time, established an SCIR model and applied it to six districts of Xiamen City for data fitting. The study further evaluated its transmissibility and provided a basis for the formulation of prevention and control measures for hepatitis C.

Index of transmissibility

In this study, the basic regeneration numbers R 0 and MNI were used to estimate the transmissibility of infectious diseases. These two indicators can minimise the errors caused by the difference in the stage of infection between chronic cases and acute cases. The innovative of this paper is to use the MNI, domestic rarely used transmissibility index, combined with data from our country's system of infectious diseases for HCV incidence in 2004–2018. According to the changing trend of infectious disease incidence, the data combined with a mathematical model, can more accurately evaluate effectiveness of some prevention and control measures.

Model validity

According to the goodness of fit test between the number of monthly morbidity fitted by the model and the actual monthly morbidity, we observed that the fitting results of the six districts in Xiamen were statistically significant (P < 0.001). At the same time, only chronic cases were included in the study model, which could avoid the error caused by the discrepancy in the stage of infection between chronic cases and acute cases. In addition, the basic regeneration number R 0, an indicator of hepatitis C transmissibility, represents the number of new cases directly transmitted within the infectious period of a source of infection. The number of new cases transmitted every month, MNI, can predict the average number of new infections transmitted by an infected individual within a month, and simplify the prediction index.

Epidemiological characteristics

According to the results (Fig. 1), before 2012, there were more cases of acute hepatitis C than chronic hepatitis C. But after 2012, there were more cases of chronic hepatitis C than acute hepatitis C. The possible cause of this situation is that, with the introduction of a series of policies for prevention and control of hepatitis C in China, the incidence of acute hepatitis C has been effectively controlled, and the growth rate of acute hepatitis C cases has gradually decreased. However, the previous acute hepatitis C cases were further transformed into chronic hepatitis C cases, and the decrease in mortality caused by the improvement in the level of treatment for chronic hepatitis C gradually increased the number of chronic hepatitis C cases.

According to the results (Fig. 3), the interval between onset and diagnosis showed a general decreasing trend from 2004 to 2018. A faster diagnosis reflects the improvement of China's diagnosis and treatment system, and the change of people's concept of hepatitis C infection makes diagnosis and treatment more timely. With the progress of the medical and health system, the prevention and treatment of hepatitis C in China will be more successful.

It is known that the main route of transmission of hepatitis C cases is blood transmission, and the susceptibility factors are drug abuse by common injection equipment, unhygienic blood transfusion equipment and irregular blood donation channels [Reference Corson, Greenhalgh and Hutchinson14, Reference Martin, Hickman and Hutchinson25–Reference Vickerman, Hickman and Judd28]. In the future prevention and treatment of hepatitis C, we should take a strict inspection of drug equipment, focusing on the supervision of blood donation institutions, in order to prevent this aspect of infection.

Assessment of the transmissibility of hepatitis C

R 0 value and MNI value were used to evaluate the transmissibility of hepatitis C. According to the model's prediction, the median value of R 0 in the six districts of Xiamen was 0.4059, that is, the number of new cases directly transmitted within the infectious period of a source of infection was 0.4059. The median MNI was 0.0020, meaning that a known case of hepatitis C can infect 0.0020 patients in a month. Combined with the R 0 curve of transmissibility of hepatitis C in the six districts of Xiamen City, the number of cases of hepatitis C has decreased in recent years. As can be seen from the MNI annual average trend chart of Xiamen City, the incidence of hepatitis C declined after 2012, indicating that under the control of current prevention and control measures of hepatitis C in China, the incidence of hepatitis C decreased yearly. Finally, the incidence of hepatitis C could be controlled at a lower level.

Breban et al. found that Egypt had an R 0 of 3.54 without any intervention factors [Reference Breban16]. Compared with the conclusion of this study that the median R 0 of each district in Xiamen is 0.4059, the current transmissibility of hepatitis C in China is lower than that in Egypt without intervention. Although Egypt and China are both developing countries, due to a better living habits and more strict control of the government and residents towards drug use, China has a lower incidence of hepatitis C through drug injections. At the same time, the level of economic development may also affect the transmissibility of hepatitis C. For example, the transmissibility of hepatitis C in Xiamen is similar to that of Iceland [Reference Scott29]. Xiamen is an economically developed city in China, with higher medical and health standards, and more secure invasive medical procedures.

Due to the high price of direct-acting antiviral drugs for hepatitis C treatment [Reference Heffernan12], most patients cannot bear the economic burden involved in its treatment. In China, drugs for treatment of hepatitis C have not been used on a large scale, given that the model used in this study appropriated to the actual situation of hepatitis C treatment in China; as a result, the factors involved in the treatment of hepatitis C have not been considered.

And we found in the study of adding intervention factors that if everyone in Egypt follows the average behaviour (2.1 injections and 0.23 invasive medical procedures per year), that is, R 0 is 0.64 without treatment based only on high-risk behaviour control [Reference Breban16]. If the measures for prevention and treatment of individuals were focused on reducing the number of chronic infections that result due to high rate of medical injections, then the value of R 0 could be lower than 1. With the expansion of the treatment scale in Iceland, the basic reproduction number of HCV dropped from 1.08 to 0.59 [Reference Scott29]. Currently, a small number of places in China have started drug treatment plans, but because we are unable to obtain detailed data, this study has not yet added intervention factors related to treatment or prevention and control, so our study may overestimate the transmissibility of hepatitis C in Xiamen City. The next step of our research is to investigate the effectiveness of treatments and prevention and control measures, to establish models for drugs and prevention and control measures, to evaluate the effectiveness of hepatitis C treatment, and to explore a more accurate trend for the transmissibility of hepatitis C in China.

Limitations

The purpose of the study was to determine whether the model could correctly estimate the future incidence of hepatitis C in China, and to apply the model to the incidence of hepatitis C in China with different environmental factors. In this study, data from only six districts of Xiamen were included in the model, which inevitably resulted in the deviation of fitting degree and expectation. In the future study, the data of different provinces and cities can be added to better the fitting effect. Although the SICR model fitting effect shows that the coefficient of determination is statistically significant, the coefficient of determination is however small (0.193–0.440), which may be related to the low number of cases in each region.

According to the curve of the annual median change of R 0 in each region, it can be seen that before 2009, R 0 was at a low level, and after 2009, R 0 suddenly increased to a higher level. The reason for this phenomenon is that, as shown in the epidemiological characteristic chart, there were many unclassified cases from 2004 to 2009, and the P value used to fit the model was not included in the unclassified cases, so R 0 was at a low level. As the number of years increases, the data classification becomes more detailed, so the prediction of the model becomes more stable, thus the value of R 0 increases. Based on the above inference, the R 0 value calculated in this study may be underestimated.

In the past few years, Chinese drugs for treatment of hepatitis C have been expensive, and the availability of specific drugs for hepatitis C patients is not very high, so the cure rate of hepatitis C in China is low. Due to the above factors, reinfection accounts for a very low proportion of all hepatitis C infections, so the reinfection factor of hepatitis C has not been considered in this study. However, in terms of the current status of global hepatitis C infection, drug injection is the main cause of HCV infection, and drug users are high-risk groups of hepatitis C reinfection. This shows that there are still reinfections on a global scale. According to the study of Nazrul Islam MBBS [Reference Islam, Krajden and Shoveller30], the rate of hepatitis C reinfection is approximately 1.27 per 100 person-years (95% CI 1.15–1.39). The systematic review of hepatitis C reinfection by Bart P. Grady shows that in the six studies that followed up person-year (PY) data, the reinfection rate ranged from 0.8 to 4.7 per 100 PY. Therefore, the reinfection of hepatitis C is one of the factors that have to be considered when constructing the hepatitis C transmission dynamics model. In this study, all the HCV infection was attributed to the contact of susceptible people with the source of infection, which may overestimate the occurrence of this situation, and therefore may overestimate the transmissibility of hepatitis C in Xiamen City. The focus of our future research is to build a model that adds hepatitis C reinfection factors, determine the proportion coefficient of hepatitis C reinfection in China and predict the transmissibility that is more in line with local actual conditions.

Conclusion

This study used R 0 and new indicator MNI to quantify the transmissibility of HCV by fitting the data of HCV incidence in six districts of Xiamen City. The data fitting effect of each district was good, which could be extended to the whole country for the study of HCV incidence. According to the fitting curve that demonstrates how changes in transmissibility occur over time for hepatitis C, transmissibility for hepatitis C in Xiamen's municipal districts exhibits a decreasing trend, and the average transmissibility is also on the decline, thus, it can be predicted that under the current preventive and control measures, future incidence rate will gradually reduce, making it possible for the incidence of hepatitis C to be controlled at a lower level.

Acknowledgements

The authors thank all study participants for providing the data and field investigators for collecting the data. We thank the support from Undergraduate Innovation Practice Platform of School of Public Health, Xiamen University.

Author contributions

TC, BZ and YS designed the study. MW collected data. TC, WY, MW, MNH, QH, ZZ, JR, XL, YZ, JX, MY and JC analysed the data. TC, YW, ZZ, MNH and QH wrote the first draft of this paper. All authors contributed to the writing of the manuscript.

Financial support

This study was partly supported by the Open Research Fund of State Key Laboratory of Molecular Vaccinology and Molecular Diagnostics (SKLVD2019KF005), the Bill & Melinda Gates Foundation (INV-005834), the Science and Technology Program of Fujian Province (No. 2020Y0002), the Xiamen New Coronavirus Prevention and Control Emergency Tackling Special Topic Program (No. 3502Z2020YJ03) and NHC Key Laboratory of Echinococcosis Prevention and Control (No. 2020WZK2001).

Conflict of interest

The authors declare that there are no conflicts of interest.

Data availability statement

The datasets used and analysed during the current study are available from Dr Mingzhai Wang () on reasonable request.

Footnotes

*

These authors contributed equally to this study.

References

Webster, DP, Klenerman, P and Dusheiko, GM (2015) Hepatitis C. Lancet (London, England) 385, 1124–1135.CrossRefGoogle ScholarPubMed
Shi, J et al. (2017) Current progress in host innate and adaptive immunity against hepatitis C virus infection. Hepatology International 11, 374–383.CrossRefGoogle ScholarPubMed
Taherkhani, R and Farshadpour, F (2017) Global elimination of hepatitis C virus infection: progresses and the remaining challenges. World Journal of Hepatology 9, 1239–1252.CrossRefGoogle ScholarPubMed
Jacobson, IM et al. (2011) Telaprevir for previously untreated chronic hepatitis C virus infection. New England Journal of Medicine 364, 2405–2416.CrossRefGoogle ScholarPubMed
hepatitis C Available at http://www.who.int/en/news–room/fact–sheets/detail/hepatitis–c.Google Scholar
Mohsen, A et al. (2015) Hepatitis C virus acquisition among Egyptians: analysis of a 10-year surveillance of acute hepatitis C. Tropical Medicine and International Health 20, 89–97.CrossRefGoogle ScholarPubMed
Khan, AJ et al. (2000) Unsafe injections and the transmission of hepatitis B and C in a periurban community in Pakistan. Bulletin of the World Health Organization 78, 956–963.Google Scholar
Mitruka, K et al. (2015) Launch of a nationwide hepatitis C elimination program – Georgia, April 2015. MMWR-Morbidity and Mortality Weekly Report 64, 753–757.Google ScholarPubMed
Cui, JA et al. (2020) Global dynamics of an epidemiological model with acute and chronic HCV infections. Applied Mathematics Letters 103, 106203.Google Scholar
Li, J et al. (2015) Dynamical analysis on a chronic hepatitis C virus infection model with immune response. Journal of Theoretical Biology 365, 337–346.CrossRefGoogle ScholarPubMed
Shi, R and Cui, Y (2016) Global analysis of a mathematical model for hepatitis C virus transmissions. Virus Research 217, 8–17.CrossRefGoogle ScholarPubMed
Heffernan, A et al. (2019) Scaling up prevention and treatment towards the elimination of hepatitis C: a global mathematical model. Lancet (London, England) 393, 1319–1329.CrossRefGoogle ScholarPubMed
Elbasha, EH (2013) Model for hepatitis C virus transmissions. Mathematical Biosciences and Engineering 10, 1045–1065.Google ScholarPubMed
Corson, S, Greenhalgh, D and Hutchinson, S (2012) Mathematically modelling the spread of hepatitis C in injecting drug users. Mathematical Medicine and Biology 29, 205–230.CrossRefGoogle ScholarPubMed
Castro Sanchez, AY et al. (2013) A mathematical model for HIV and hepatitis C co-infection and its assessment from a statistical perspective. Epidemics 5, 56–66.CrossRefGoogle ScholarPubMed
Breban, R et al. (2014) Effect of preventive and curative interventions on hepatitis C virus transmission in Egypt (ANRS 1211): a modelling study. Lancet Global Health 2, E541–E549.CrossRefGoogle ScholarPubMed
Pan, S and Chakrabarty, SP (2018) Threshold dynamics of HCV model with cell-to-cell transmission and a non-cytolytic cure in the presence of humoral immunity. Communications in Nonlinear Science and Numerical Simulation 61, 180–197.CrossRefGoogle Scholar
Hart, GR and Ferguson, AL (2018) Computational design of hepatitis C virus immunogens from host-pathogen dynamics over empirical viral fitness landscapes. Physical Biology 16, 016004.CrossRefGoogle ScholarPubMed
Kitagawa, K et al. (2018) A PDE multiscale model of hepatitis C virus infection can be transformed to a system of ODEs. Journal of Theoretical Biology 448, 80–85.CrossRefGoogle ScholarPubMed
Zhang, S et al. (2020) Transmissibility of acute haemorrhagic conjunctivitis in small-scale outbreaks in Hunan Province, China. Scientific Reports 10, 119.CrossRefGoogle ScholarPubMed
Zheng, YL et al. (2015) Forecast model analysis for the morbidity of tuberculosis in Xinjiang, China. PLoS One 10, e0116832.CrossRefGoogle ScholarPubMed
Liu, L et al. (2016) Predicting the incidence of hand, foot and mouth disease in Sichuan province, China using the ARIMA model (vol 144, pg 144, 2015). Epidemiology and Infection 144, 152–152.CrossRefGoogle Scholar
Longini, IM et al. (2005) Containing pandemic influenza at the source. Science (New York, N.Y.) 309, 1083–1087.Google ScholarPubMed
Hutchinson, SJ et al. (2015) Expansion of HCV treatment access to people who have injected drugs through effective translation of research into public health policy: Scotland's experience. International Journal of Drug Policy 26, 1041–1049.CrossRefGoogle ScholarPubMed
Martin, NK, Hickman, M and Hutchinson, SJ (2014) Combination interventions to prevent HCV transmission among people who inject drugs: modeling the impact of antiviral treatment, needle and syringe programs, and opiate substitution therapy (vol 57, pg s39, 2013). Clinical Infectious Diseases 58, S39–S45.Google Scholar
Mather, D and Crofts, N (1999) A computer model of the spread of hepatitis C virus among injecting drug users. European Journal of Epidemiology 15, 5–10.CrossRefGoogle ScholarPubMed
Sutton, AJ et al. (2006) Modelling the force of infection for hepatitis B and hepatitis C in injecting drug users in England and Wales. BMC Infectious Diseases 6, 93.CrossRefGoogle ScholarPubMed
Vickerman, P, Hickman, M and Judd, A (2007) Modelling the impact on hepatitis C transmission of reducing syringe sharing: London case study. International Journal of Epidemiology 36, 396–405.CrossRefGoogle ScholarPubMed
Scott, N et al. (2018) Modelling the elimination of hepatitis C as a public health threat in Iceland: a goal attainable by 2020. Journal of Hepatology 68, 932–939.CrossRefGoogle ScholarPubMed
Islam, N, Krajden, M and Shoveller, J (2017) Incidence, risk factors, and prevention of hepatitis C reinfection: a population-based cohort study (vol 2, pg 200, 2017). Lancet Gastroenterology & Hepatology 2, E2–E2.CrossRefGoogle Scholar
Figure 0

Fig. 1. Flow chart of SICR model.

Figure 1

Fig. 2. Annual trends of acute, chronic and unclassified morbidity.

Figure 2

Fig. 3. Incidence rates by gender for each year.

Figure 3

Fig. 4. Mean time interval between time of onset and diagnosis (in months).

Figure 4

Fig. 5. Statistical chart of annual incidence of hepatitis C in various districts of Xiamen City.

Figure 5

Fig. 6. Results of model fitting curve and actual case change curve.

Figure 6

Fig. 7. R0 and MNI were used to represent the transmissibility of hepatitis C in six districts of Xiamen City. (a) The curve of the median of R0; (b) the curve of the median of MNI.

Figure 7

Fig. 8. Variation trend of median, minimum and maximum value of R0 in Xiamen.

Figure 8

Fig. 9. Variation trends of median, minimum and maximum of MNI values in Xiamen.

Figure 9

Table 1. Estimation of fitting degree curve between model and actual situation

Figure 10

Fig. 10. Trend of R0 value of hepatitis C transmissibility fitting curve by time. (a) The cubic curve; (b) the compound curve and (c) the power function curve.

Figure 11

Table 2. Various curve fitting results of R0 value

Figure 12

Fig. 11. Trend of MNI value of hepatitis C transmissibility fitting curve by time. (a) The cubic curve; (b) the compound curve and (c) the power function curve.

Figure 13

Table 3. Results of various curve fittings of MNI values