Viral infection model with diffusion and state-dependent delay: a case of logistic growth

Abstract

We propose a virus dynamics model with reaction-diffusion and logistic growth terms, intracellular state-dependent delay and a general non-linear infection rate  functional response. Classical solutions with Lipschitz in-time initial functions are investigated. This type of solutions is adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions approach is used to analyse stability of interior infection equilibria which describe the cases of a chronic disease.