Stability of delayed discrete-time viral model with antibody and cell-mediated immune responses

Abstract

We propose a discrete-time viral model with antibody and cell-mediated immune responses. Two types of infected cells are incorporated into the model, namely latently infected and actively infected. The model incorporates three types of intracellular time delays. We use nonstandard finite difference (NSFD) method to discretize the continuous-time model. We prove that NSFD preserves the positivity and boundedness of the solutions of the model. Based on four threshold parameters the existence of five equilibria is established. We perform global stability of all equilibria of the model by using Lyapunov approach. Numerical simulations are carried out to illustrate our theoretical results. The impact of time delay on the viral dynamics is established.

Keywords

• Viral dynamics
• Latency
• Time delay
• Gobal stability
• Antibody
• Cell-mediated response