Motivations: Hepatitis B is a potentially life-threatening infectious disease caused by the hepatitis B virus (HBV). Approximately 390,000 people in China die from HBV-related diseases each year. Around 86 million individuals suffer from infections of the hepatitis B virus, accounting for about 6% of the total population in the region. There are approximately 30 million chronic infections. From 2002 to 2007, China’s government took part in “The Global Alliance for Vaccines and Immunization (GAVI)” initiative, which helped reduce cases of chronic HBV infections among children. However, incidences of hepatitis B remain persistently high in China. Accurately estimating the number of potential HBV infections is crucial for preventing and controlling the transmission of the hepatitis B virus. Up until now, there were no studies of potentially infectious hepatitis B virus infections. Methods: this study was based on data from the National Bureau of Statistics of China from 2003 to 2021; a dynamic model was built, which included a compartment for potentially infectious hepatitis B virus infections. The parameters in the model were fitted using a combination of nonlinear least-squares and genetic algorithm methods. Results: the calculated reproduction number for hepatitis B virus transmission within the population is $R_c$ = 1.741. Considering the existing vaccine inefficiency rate of 0.1, the model estimates there are 449,535 (95%CI [415,651, 483,420]) potentially infectious hepatitis B virus infections, constituting 30.49% of total hepatitis B cases. Date fitting using MATLAB reveals that increasing the rate of hepatitis B vaccinations can effectively reduce the number of infections. Conclusions: the results reveal that the number of potential infectious hepatitis B virus infections is so high that the number of hepatitis B patients persistently rises in China. To better control the transmission of the hepatitis B virus, an optional prevention and control strategy is needed to increase the vaccination of different age groups, and it is necessary to help the public correctly understand the transmission of hepatitis B and ensure adequate protection.

Hepatitis B is a potentially life-threatening infectious disease caused by the hepatitis B virus (HBV), which affects the liver. Every year, about 390,000 people die from HBV-related diseases in China, about 86 million people are carriers of HBV, accounting for about 6% of the total population, and 30 million people are chronically infected. From 2002 to 2007, though China government launched “The Global Alliance for Vaccines and Immunization (GAVI)” program to reduce HBV infection in children, but the number of hepatitis B cases in China remains high. Reasonable estimation of potential HBV carriers is crucial to prevention and control the spread hepatitis B virus. This study is based on the case data from the National Bureau of Statistics of China from 2003 to 2021. We build a dynamic model that includes potential hepatitis B virus carriers, use nonlinear least squares and genetic algorithms to fit the parameters in the model, and calculate the reproduction number of hepatitis B virus transmission in the population and obtain R_c=1.741. The number of potential hepatitis B virus carriers is estimated to be 449,535 (95%CI [415651 to 483420]) based on our model, which is 30.49% of the total number of hepatitis B cases, and the simulation results show the number of chronic hepatitis B incidence decreases as the vaccination rate α increases, increasing α by 20%, the number of chronic hepatitis B incidence decreases by 169,469 on average.

MotivationAIDS is a chronic and fatal infectious disease caused by the human immunodeficiency virus (HIV). According to the Chinese Center for Disease Control and Prevention (CDC), there are currently 689, 000 cases of HIV-infected patients, with 103, 350 new HIV infections in 2019 and the number of HIV cases continues to rise. Therefore, a reasonable estimation of the number of potentially HIV-infected individuals in the population is essential for the prevention and control of AIDS. MethodWe develop a dynamic model of a compartment containing potential HIV-infected individuals and fitted the parameters of the model using nonlinear least squares based on the data from 2004 to 2019. ResultsThe basic reproduction number of the model is calculated to be $ R_0 $=1.514 and the mean number of potential HIV-infected individuals in the population is estimated by the model to be 16847 (95$ \% $CI [15047, 18846]). In 2004, there are 1.7835 times more potential HIV-infected individuals K than HIV-infected individuals, this then decreases each year. The average ratio of potentially HIV-infected individuals to HIV-infected individuals from 2004 to 2019 is 38.41$ \% $. ConclusionsThe number of potential HIV-infected individuals has an important impact on the transmission and control of HIV virus and the proportion of changing sexual behavior habits can greatly reduce the number of new potential HIV-infected individuals. The existence of potential HIV-infected individuals should be taken into account in prevention and control strategies and publicity efforts should be intensified so that more people can understand the transmission pathways, pathogenesis and precautions against AIDS, in order to better reduce the number of new HIV infections and the spread of HIV virus in the population.