Hopf Bifurcation Analysis In A Delayed HIV Pathogenesis Model With Stage-Structure

HIV is a kind of lentivirus which infect of the human immune system, it infect thehuman T4 cells, trigger damage of the whole immune system, lead to HIV infector'simmune function failure, consequently disease and cancer may be survive in the humanbody, and finally development to lead to AIDS.Since 1985 when reports came from Peking Union Medical College Hospital foundthe first AIDS virus infector to the first half of 2009 in China, the total number who in-fected from AIDS virus has risen to nearly 1 million, becoming one of the fastest growingcountry of AIDS infection rates in the world. According to data released by the ministryof health in 2009, AIDS is spreading quickly from high-risk groups to the general popula-tion and become one of the first infectious diseases that cause death. Therefore, study thepathogenesis of HIV so that to find factors which cause HIV and then predict and controlit has become the urgent research topic.Firstly, this paper introduce and analysis the HIV pathogenesis model and its history,then considered a delayed HIV pathogenesis model with stage-structure proposed by WuJianhong under the classical HIV model. After that analysed the stability of equilibriumand the existence of local Hopf bifurcation by discussing the characteristic equation of theequilibrium, then give several mathematical formulas about some parameters, which pro-vide some informations to estimate the analytical properties of the Hopf bifurcation, withthe help of the normal form method and center manifold theory. Finally, use Simulinkpackage in Matlab do numerical simulations to support the preceding theoretical analysis.