Mathematical modelling of the role of interference on the transmission dynamics and management of Hiv and Aids

Abstract

In this paper, a deterministic mathematical model incorporating interference is developed andanalysed to investigate the role of interference on the transmission dynamics and managementof HIV and AIDS. The model is shown to be positively invariant as well as bounded. Theendemic state is shown to exist provided that the reproduction number is greater than unity.Furthermore, by the use of Routh-Hurwitz criterion and suitable Lyapunov functions, theendemic states are shown to be locally and globally asymptotically stable. This implies thatdisease transmission levels can be kept quite low or manageable with minimal deaths at the peaktimes of the re-occurrences. Numerical simulations indicate that minimal interference againstthe disease lowers the rate of infection and enhances the disease management.