Background With expanded access to antiretroviral therapy (ART) in sub-Saharan Africa, HIV mortality has decreased, yet life-years are still lost to AIDS. Strengthening of treatment programmes is a priority. We examined the state of an HIV care programme in Kenya and assessed interventions to improve the impact of ART programmes on population health. Methods We created an individual-based mathematical model to describe the HIV epidemic and the experiences of care among adults infected with HIV in Kenya. We calibrated the model to a longitudinal dataset from the Academic Model Providing Access To Healthcare (known as AMPATH) programme describing the routes into care, losses from care, and clinical outcomes. We simulated the cost and effect of interventions at different stages of HIV care, including improvements to diagnosis, linkage to care, retention and adherence of ART, immediate ART eligibility, and a universal test-and-treat strategy. Findings We estimate that, of people dying from AIDS between 2010 and 2030, most will have initiated treatment (61%), but many will never have been diagnosed (25%) or will have been diagnosed but never started ART (14%). Many interventions targeting a single stage of the health-care cascade were likely to be cost-effective, but any individual intervention averted only a small percentage of deaths because the effect is attenuated by other weaknesses in care. However, a combination of five interventions (including improved linkage, point-of-care CD4 testing, voluntary counselling and testing with point-of-care CD4, and outreach to improve retention in pre-ART care and on-ART) would have a much larger impact, averting 1??10 million disability-adjusted life-years (DALYs) and 25% of expected new infections and would probably be cost-effective (US$571 per DALY averted). This strategy would improve health more efficiently than a universal test-and-treat intervention if there were no accompanying improvements to care ($1760 per DALY averted). Interpretation When resources are limited, combinations of interventions to improve care should be prioritised over high-cost strategies such as universal test-and-treat strategy, especially if this is not accompanied by improvements to the care cascade. International guidance on ART should reflect alternative routes to programme strengthening and encourage country programmes to evaluate the costs and population-health impact in addition to the clinical benefits of immediate initiation.