Stability analysis of a delay differential equation describing the antiviral immune response

The aim of this work is to study the dynamics of viral infection by a mathematical model using a differential equation with a single delay corresponding to the duration of proliferation and differentiation of immune cells and the time required to program activated CTLs. Asymptotic and global stability conditions for the considered delayed differential equation are defined in order to study the asymptotic behaviour of the solutions. Key theorems are proven using the theory of monotone dynamical systems, mainly the results established by M. Pituk in 2003. Sufficient conditions of stability of the nonzero equilibrium have been established and formulated in terms of the efficiency and delay of the immune response. Numerical simulations of the model are given to validate analytical results.