Occurrence vs. Absence of taxis-driven instabilities in a May-Nowak model for virus infection

This work focuses on an extension to the May-Nowak model for virus dynamics, additionally accounting for diffusion in all components and chemotactically directed motion of healthy cells in response to density gradients in the population of infected cells. The first part of the paper presents a number of simulations with the aim of investigating how far the model can depict interesting patterns. A rigorous analysis of the initial-boundary value problem is presented in a second part, where a statement on global classical solvability for arbitrarily large initial data is derived under an appropriate smallness assumption on the chemotactic coefficient. Two additional results on asymptotic stabilisation indicate that the so-called basic reproduction number retains its crucial influence on the large time behavior of solutions, as is well-known from results on the May-Nowak system.