Since 2000, there has been a substantial global reduction in the vertical transmission of HIV. Despite effective interventions, gaps still remain in progress towards elimination in many low-income and middle-income countries. We developed a mathematical model to determine the most cost-effective combinations of interventions to prevent vertical transmission. We developed a 12-month Markov model to follow a cohort of women of childbearing age (aged 15-49 years) in Zambia (n=1 107 255) who were either pregnant, in delivery, or breastfeeding; the population included in the model reflects the estimated number of pregnant women in Zambia from the 2018 Zambia Demographic and Health Survey. The model incorporated nine interventions: infant prophylaxis; three different HIV retesting schedule options; oral pre-exposure prophylaxis; maternal peer-support groups; regimen shift; tracing of loss to follow-up; and point-of-care viral load testing. We analysed incident HIV infections among mothers and infants, intervention costs, and evaluated 190 scenarios of different combinations of inventions to calculate the incremental cost-effectiveness ratios (ICERs) over 1 year. Three interventions with the greatest reduction in vertical transmission, individually, were support groups for 80% of those in need (35% reduction in infant infections), HIV retesting schedules (6·5% reduction), and infant prophylaxis (4·5% reduction). Of all 190 scenarios evaluated, eight were on the cost-effectiveness frontier (ie, were considered to be cost-effective); all eight included increasing infant prophylaxis, regimen shift, and use of support groups. Excluding the highest-cost scenarios, for a 1-22% increase in total budget, 23-43% of infant infections could be prevented, producing ICERs between US$244 and $16 242. Using the interventions modelled, it is possible to reduce vertical transmission and to cost-effectively prevent up to 1734 infant HIV infections (43% reduction) in Zambia over a period of 1 year. To optimise their effect, these interventions must be scaled with fidelity. Future work is needed to incorporate evidence on additional innovative interventions and HIV risk factors, and to apply the model to other country contexts to support targeted implementation and resource use. The ELMA Foundation.