Dotia, A.K.Ibrahim, M.O.Abubakar, Jos U.2023-05-252023-05-252017-05https://uilspace.unilorin.edu.ng/handle/20.500.12484/10793We present a time-dependent HBV epidemic model with both prophylactic and therapeutic vaccination. This epidemic model is investigated for different classes of infectious diseases. Mathematical analyses are carried out, that determines the positivity of solution and an optimal control approach is applied in order to find the best way to fight the disease. An optimal control strategy in the form of vaccination, and to minimize or eradicate the mother to child transmission is used. The study concluded that both prophylactic and therapeutic vaccination are efficient ways to curb the epidemic.enVaccination, optimal control, epidemic, time-dependentArticle