Dynamical analysis and optimal control for a delayed viral infection model

Abstract

To describe the interaction between viral infection and immune response, we establish a mathematical model with intracellular delay and investigate an optimal control problem to examine the effect of antiviral therapy. Dynamic analysis of the proposed model for the stability of equilibria and Hopf bifurcation is conducted. Theoretical results reveal that the dynamical properties are determined by both the immune-inactivated reproduction number and the immune-activated reproduction number. With the aim of minimizing the infected cells and viral load with consideration for the treatment costs, the optimal solution is discussed analytically. Numerical simulations are performed to suggest the optimal therapeutic strategy and compare the model-predicted consequences.