BackgroundHepatitis B (HB) is a virus which causes a potentially fatal liver infection. It is a DNA virus belonging to the Hepadnaviridae virus family. Africa, after Asia, has the second highest number of chronic HBV carriers and is considered a high-endemic region. Ethiopia is classified as a country with a high prevalence of viral hepatitis and with nations that lack a systematic strategy for viral hepatitis surveillance.MethodsS-I-C-R deterministic model was developed and the numerical simulations were done in “R” statistical and programming software. Fixed population assumption was considered so as to develop a simple model which could predict the HBV vertical transmission for the next 5 decades.ResultsThe model revealed that significant number of populations will be infected and become carrier till the end the next 49 years even though it has decreasing trend. It was predicted that 271,719 people will die of HBV complications if no intervention will be made on its vertical transmission. The sensitivity analysis result showed that the force of infection has the most important parameter in the vertical transmission dynamics of hepatitis B. Provision of hepatitis B immunoglobulin (HBVIG) and vaccines at the time of delivery could decrease the force of infection by more than half and 51,892 lives will be saved if the intervention is offered for 50% of deliveries in Ethiopia.ConclusionDespite the fact that the incidence of HBV vertical transmission is substantial, it is expected to decline during the next five decades. However, the situation necessitates immediate attention, since it results in thousands of deaths if no action is taken. Offering HBVIG and vaccinations to the 50% of infants can save many lives and reduces the force of infection by more than a half.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12879-023-08343-4.