An epidemiological model is proposed and studied to understand the
transmission dynamics and prevalence of HCV infection in China.
Theoretical analysis indicates that the basic reproduction number
Hepatitis C virus (HCV) has been considered as a leading cause of liver cirrhosis and hepatocellular carcinoma and is becoming a major and growing global health problem [
Mathematical models have been used to analyze the spread and control of HCV infection in [
The purpose of this study is to formulate a mathematical model which involves almost all possible stages during HCV infection with the aim of accessing the potential impact of antiviral treatment on HCV prevalence of China and then providing reliable quantitative information on controlling the HCV epidemic in China. On the basis of the model in [
The paper is organized as follows. In Section
We propose a mathematical model to understand the transmission dynamics and prevalence of HCV in mainland China using a system of ordinary differential equations. The population are divided into six classes:
Parameters and initial data chosen for the simulation.
Variable and parameter  Description  Initial or default values  Source 

Variables  

Susceptible population 

LS 

Exposed population  4187  LS 

Acutely infected population  151360  LS 

Chronically infected population 

LS 

Treated population  50000  LS 

Recovered population with partial immunity 

LS 
Parameters  

Recruitment rate 

See text 

Natural death rate  0.007 year^{−1}  [ 

Transmission rate of acutely infected population 

LS 

Transmission rate of chronically infected population 

LS 

Transmission rate of treated population 

LS 

Rate of progression to acute stage from the exposed  6 year^{−1}  [ 

Recovery rate for the acute state  0.5 year^{−1}  [ 

Rate of moving from acute stage to chronic stage  4 year^{−1}  [ 

Treatment rate of acutely infected population  0.1545 year^{−1}  see text 

Treatment rate of chronically infected population  0.04 year^{−1}  [ 

Treatment cure rate  0.67 year^{−1}  [ 

Treatment failure rate  0.82 year^{−1}  [ 

HCV induced death rate at the chronic stage  0.001 year^{−1}  [ 

Rate of waning immunity  0.025 year^{−1}  [ 
LS, least square.
A schematic flow diagram illustrating the transmission dynamics of the HCV infection with treatment.
Since
To investigate the effect of therapy, we study variation in the basic reproduction number
Regardless,
Model (
(i) If
(ii) If
(i) Construct a continuously differentiable and positive definite Lyapunov function
In the domain
(ii) The Jacobian matrix of system (
Define
Next we claim that there exists a positive constant
The global stability of the endemic equilibrium is studied under the simplified assumption that the immune loss rate is zero (i.e.,
When
Construct a continuously differentiable and nonnegative Lyapunov function:
Differentiating
Obviously,
In order to assure
The annual reported HCV case numbers have been released by the National Health and Family Planning Commission of China [
(a) Annual newly reported HCV cases for mainland China; (b) goodness of fit and prediction of HCV trends until 2021. Stars represent the reported number of people with HCV by year. The solid line shows the fit based on the current circumstances (
Using the estimated parameter values we calculated the basic reproduction number
Plots of the prevalence against time at varying parameter values: (a) the treatment rate
To examine the impact of treatment on HCV transmission dynamics and prevalence and identify the most effective measures to control the transmission of HCV in mainland China we investigated variation in the basic reproduction number and prevalence (i.e.,
To access the effectiveness of treatment interventions in the long term, we examine the effects of the corresponding treatment parameters
(a) Plots of the basic reproduction number
To examine the sensitivity of our results to parameter variation, we used Latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCCs) [
PRCC values for
Input parameters  Distributions 

Prevalence  

PRCC 

PRCC 




0.0395  0.0781  0.0337  0.1328 


0.7609  0  0.4823  0 


0.4123  0  0.2284  0 


−0.8065  0  −0.7549  0 


−0.0311  0.1645  −0.0380  0.0902 


−0.7644  0  −0.7151  0 


0.0386  0.0845  0.2219  0 


—  —  0.6550  0 
(a) PRCCs of the eight parameters for prevalence from 2003 to 2021. (b) PRCCs for
In order to understand the prevalence of HCV infection in China based on the reported data [
When the model was applied to HCV transmission in China, we estimated the basic reproduction number
It follows from sensitivity analysis (Figure
It should be acknowledged that one limitation of our results is that the reported national data may not be completely composed of exposed people who enter into the acute stage. The data may contain some cases diagnosed at the acute or chronic stage; though the number of these cases is low, it may still result in a slight overestimate of the prevalence of HCV in China. However, the slightly overestimated results were not caused by our model, but rather by the deficiency of data which did not distinguish which stage the reported cases came from. More realistic models about HCV infection on complex networks [
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors thank Professor Robert A. Cheke for his helpful comments on the paper. The authors are supported by the National Natural Science Foundation of China (11171268 (Yanni Xiao)) and by the Fundamental Research Funds for the Central Universities (08143042 (Yanni Xiao)).