Propagation dynamics for a spatial discrete virus model with HIV viral load and 2-LTR dynamics

This paper considers the wave propagation for a spatial discrete virus model with HIV viral load and 2-LTR dynamics during high active antiretroviral therapy. Applying Schauder fixed point theorem, technique of Lyapunov function and limiting arguments, we establish the existence of traveling wave solutions for the virus model when the basic reproduction number is larger than one and the wave speed is not less than a threshold speed. Then, using the methods of comparison principle and Laplace transform, we prove the nonexistence of traveling wave solutions when the basic reproduction number is either smaller than one; or larger than one but the wave speeds are less than the threshold speed. Indeed, the threshold speed is minimum wave speed for the propagation of traveling waves. We further show that the three classes of inhibitor can decrease the minimum wave speed; while the diffusion rate of visions will increase the minimum wave speed.