Threshold dynamics of a diffusive HIV infection model with infection-age, latency and cell–cell transmission

This work intends to analyze the global threshold dynamics of an HIV infection model with age-space structure, latency and two transmission paths (virus to cell and cell to cell) under the Neumann boundary condition. The original model is converted into a hybrid system comprising two Volterra integral equations and two partial differential equations by integrating along the characteristic line. The well-posedness of the model is demonstrated by showing that the solution exists globally by virtue of the fixed point theory. In order to discuss whether the infection is persistent or extinct, we provide the explicit formulation of the basic reproduction number. By analyzing the roots distribution of the characteristic equations and constructing proper Lyapunov functionals, the local and global stability for different steady states are achieved. Numerical simulations are conducted to confirm our theoretical results.