Taxis-driven Formation of Singular Hotspots in a May--Nowak Type Model for Virus Infection

A three-component reaction-diffusion system is considered which originates from an extension of the classical May--Nowak model for viral infections to situations in which spatially heterogeneous dynamics need to be accounted for. In accordance with recent developments in the modeling literature, a particular focus is on possible effects of taxis-type movement of uninfected toward infected cells, where in contrast to setting addressed by standard Keller--Segel type systems, the evolution of the considered attractant is influenced by an inherently nonlinear production mechanism. Despite the accordingly increased mathematical challenges going along with an apparent lack of favorable structural properties that have facilitated accessibility of such classical Keller--Segel models to various techniques from parabolic blow-up analysis, the present study attempts to develop an approach capable of detecting taxis-driven aggregation phenomena in complex models of this form. In the framework of radially symmetric solutions to associated Neumann-type initial boundary value problems, through an analysis of a corresponding mass accumulation function a result on the occurrence of finite-time blow-up in two- or three-dimensional balls is derived. This rigorously confirms the potential of the considered model to describe the spontaneous emergence of locally high densities, as known from experimental observations in contexts of virus hotspot formation phenomena.