We present a modelling approach for transmission and population dynamics of human T-cell lymphotropic-virus-type-I (HTLV-I) infection. A steady-state analysis of the model was used to estimate transmission rates for males and females. The rate of heterosexual transmission was 2.7 times higher if the carrier was male. A dynamic transmission model was developed and used to study the impact of different intervention measures in the Jamaican population. Interventions concerning horizontal (heterosexual) transmission exceeds the effect of breaking vertical (mother-to-child) transmission, although breast feeding also has an important impact on the total number of infected individuals.