Abstract: This paper is concerned with the transmission mechanism of hepatitis B virus between mother and infant and the inhibitory effect of hepatitis B immunoglobulin on hepatitis B virus, and the dynamics mode of blocking the transmission of hepatitis B virus between mother and infant is established. Applying Lyapunov function and composite matrix theory, the stability of equilibrium point of model is studied. The rationality of the model is analyzed by Matlab based on the clinical data of hepatitis B immunoglobulin dosage and detection of hepatitis B virus DNA. The numbers of hepatitis B virus in pregnant women with hepatitis B virus carriers and hepatitis B virus infections at different dosages are obtained by numerically simulation. Moreover, the number of hepatitis B virus in fetuses is predicted, which provides a theoretical basis for clinical medication.

Key words: hepatitis B immunoglobulin, hepatitis B virus, dynamic model of mother-to-child transmission of hepatitis B virus, stability, dosage