Global threshold dynamics and finite-time contraction stability for age-structured HIV models with delay

Abstract Considering age of infected cells and intracellular delay in both virus-to-cell and cell-to-cell transmissions, this paper develops an age-structured HIV model with delay to investigate the global threshold dynamics, which show the uninfected and infected steady states of the model. Using the Lyapunov function and LaSalle's invariance principle, we show that the global threshold dynamics of the model can be determined by utilizing basic reproduction number. Moreover, given that sudden environmental changes can lead to uncertainty in parameters of the model, a stochastic age-structured HIV model with Markovian switching is developed to study the finite-time contraction stability, which characterizes transmission properties of virus over a finite time. The sufficient conditions of the finite-time contraction stability are obtained by employing the Lyapunov function and stochastic comparison theorem. Numerical examples are presented to illustrate the theoretical results, and numerical results show that different noise intensity and delay affect stability of the HIV models.