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.

In this paper, a class of delay differential equations model of HIV infection dynamics with nonlinear transmissions and apoptosis induced by infected cells is proposed, and then the global properties of the model are considered. It shows that the infection-free equilibrium of the model is globally asymptotically stable if the basic reproduction number $R_{0}1$. Furthermore, it also shows that the model is permanent, and some explicit expressions for the eventual lower bounds of positive solutions of the model are given.

The aim of this paper is to give some global stability criteria on a variant of Lyapunov-LaSalle theorem for a class of delay di erential system.