In sub-Saharan Africa, the model of care for people who are living with HIV/AIDS has changed from hospital care to home-based care. In this paper, a mathematical model describing the dynamics of HIV transmission, hospitalization, and home-based care is constructed and analysed. The model reproduction number R(e) is determined and discussed. The equilibria are determined and analysed in terms of R(e). It is shown that if R(e)<1, the disease free equilibrium is both locally and globally asymptotically stable. The model has a unique endemic equilibrium and is locally asymptotically stable whenever R(e)>1. Five cases arise in the discussion of R(e) pertaining to intervention strategies. Numerical simulations are done to compare the impact of each strategy on the dynamics of HIV/AIDS. The model is fitted to the prevalence data estimates from UNAIDS on Zimbabwe. The implications of some key epidemiological parameters are investigated numerically. Projections are made to determine the possible long term trends of the prevalence of HIV in Zimbabwe.