A mathematical model predicting anti-hepatitis B virus surface antigen (HBs) decay after vaccination against hepatitis B

The determination of serum levels of antibodies against hepatitis B virus surface antigen (anti-HBs) after hepatitis B vaccination is currently the only simple test available to predict the decay of protection and to plan the administration of booster doses. A total of 3085 vaccine recipients of plasma-derived and recombinant vaccine have been followed for 10 years to determine the kinetics of anti-HBs production and to construct a mathematical model which could efficiently predict the anti-HBs level decline. The anti-HBs peak level was reached 68 days after the last dose of recombinant vaccine and 138 days after the last dose of plasma-derived vaccines. The age of vaccinees negatively influenced the anti-HBs levels and also the time necessary to reach the anti-HBs peak. A bilogarithmic mathematical model (log(10) level, log(10) time) of anti-HBs decay has been constructed on a sample of recombinant vaccine recipients and subsequently validated on different samples of recombinant or plasma-derived vaccine recipients. Age, gender, type of vaccine (recombinant or plasma-derived), number of vaccine doses (three or four) did not influence the mathematical model of antibody decay. The program can be downloaded at the site: http://www2.stat.unibo.it/palareti/vaccine.htm. Introducing an anti-HBs determination obtained after the peak, the program calculates a prediction of individual anti-HBs decline and allows planning of an efficient booster policy.