A. K. DotiaM. O. IbrahimC. N. EjiejiK.A. BelloB. M. AhmedB. AjanakuA. B. KazeemA. O. Lawan2026-04-272026-04-272019Vaccination, Optimal control, Epidemic, Time-dependenthttps://uilspace.unilorin.edu.ng/handle/123456789/17698In this paper, a time - dependent model of prophylactic vaccination HBV is considered. This epidemic model is being investigated for various infectious diseases classes, counsel and uncounsel. Mathematical analyzes are performed to determine the positivity and we applied an optimal control strategies in the form of vaccination to minimize or eradicate transmission from mother to child. The study concluded that prophylactic vaccination is not an efficient way to curb the epidemicenArticle