Fig. 1
Age- and time-dependent dynamic compartmental model of HBV transmission. Boxes with solid line represent compartments of the transmission process, and lines with arrowhead represent transitions and their directions. The box with dashed line is not a compartment, only representing the transient process of acute HBV infection. λa,t, age- and time-dependent force of HBV infection; qa, age-dependent proportion of acute HBV infections that become chronic; r, rate of chronic HBV infections that become immune (HBV clearance); da,t, age- and time-dependent background mortality; dAa, age-dependent mortality of acute HBV infection; dCa, age-dependent mortality of cirrhosis; dHa, age-dependent mortality of hepatocellular carcinoma; vt, vaccine coverage of newborns at a given time; pt, vaccine protection against HBV infection at a given time; θa,t, catch-up vaccine coverage during 2009 − 2011 in children born between 1994 − 2001 who missed the routine vaccination; bt, birth rate at a given time; ɛ, HBV intrauterine infection rate in infected pregnant women; Na,t, total number of people with a specific age at a given time. \(\sum\limits_{a = 15}^{49} {C_{a,t} } /\sum\limits_{a = 15}^{49} {N_{a,t} }\) denotes HBV carriage rate of women with childbearing age (15 − 49 years) at a given time