An HIV/AIDS epidemic model with media coverage, vertical transmission and time delays

In this paper, we propose and study a time-delay compartmental model for human immunodeficiency virus (HIV) transmission, a disease which may lead to an advanced stage of infection called acquired immunodeficiency syndrome (AIDS), in a sexually active population with the presence of media coverage. The inclusion of vertical transmission in the recruitment of infected individuals is also considered. Moreover, two time delays are incorporated in the model. One delay τ₁ covers the period from the time of gathering statistical data on the total number of infections in the community up to the time that these information are reported to the public through media. The other delay τ₂ corresponds to the period that an infected newborn baby reaches the age of sexual maturity. If the threshold value R₀ < 1, then the only equilibrium point is the disease-free equilibrium which is globally asymptotically stable. If the threshold values R₀ and R₀₀ are both greater than 1, then a unique endemic equilibrium exists, which is globally asymptotically stable when media coverage is not considered. When there is no vertical transmission but media coverage is considered, the system undergoes a Hopf bifurcation at some critical value of the media delay. Numerical simulations are presented to illustrate theoretical results.