Properties of Stability and Hopf Bifurcation for an Hiv/AIds Epidemic Model With Screening and Time Delay

In this paprer, we consider an HIV/AIDS epidemic model with screening and time delay. We divide the population into four subclasses, one of them is the susceptible population S and the others are HIV infectives (HIV positives that do not know they are infected) I 1 , HIV positives that know they are infected (by way of medical screening or other ways) I 2 and that of AIDS patients A . Both the disease-free equilibrium and the infected endemic equilibrium are found and their stability is investigated using stability theory of delay differential equations. The effect of delay on the stability of the endemically infected equilibrium is investigated. It is shown that the introduction of time delay in the model has a destabilizing effect on the system and periodic solutions can arise by Hopf bifurcation when using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.