A deterministic model for assessing the impact of
counselling, condom use and treatment strategies on the transmission
dynamics of HIV/AIDS in Nigeria is designed and
rigorously analysed. The model, which consists of mutuallyexclusive
compartments representing the number of counselled,
non-counselled and treated infected individuals, has a globallyasymptotically
stable disease-free equilibrium whenever the associated
reproduction number (Rc) is less than unity. Using a
Krasnoselskii sub-linearity trick and non-linear Lyapunov function
of Goh-Volterra type, in conjunction with the LaSalle Invariance
Principle, it is shown that the endemic equilibrium is
locally-and then globally-asymptotically stable for special cases.
Numerical simulations, using demographic and epidemiological
data relevant to Nigeria, show that the use of condoms, as a
singular anti-HIV intervention strategy, can lead to effective
control of HIV in Nigeria if the condom efficacy and compliance
rate in its usage are high enough (at least 80% and 65%,
respectively). Furthermore, the singular use of public health
counselling of infected individuals or anti-retroviral drugs can
lead to the effective control or elimination of HIV in Nigeria
if their effectiveness levels are moderately high enough (these
strategies could avert between 10 to 12 million new HIV cases
in Nigeria over a period of 6 years). Finally, the prospect of HIV
elimination in Nigeria is greatly enhanced if the aforementioned
strategies are implemented together (universally). A universal
strategy, with high level of effectiveness, can lead to HIV elimination
in Nigeria within 23 years.