SIAM Journal on Mathematical Analysis, Volume 53, Issue 2, Page 1411-1433, January 2021.
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.

中文翻译：

---

出租车驱动的May-Nowak型病毒感染模型中奇异热点的形成

SIAM数学分析杂志，第53卷，第2期，第1411-1433页，2021年1月。
考虑了一种三组分反应扩散系统，该系统源自病毒感染的经典May-Nowak模型的扩展到需要考虑空间异质性动力学的情况。根据建模文献的最新发展，特别关注未感染的出租车类型向感染细胞移动的可能影响，与标准的Keller-Segel类型系统解决的设置相反，认为引诱剂的进化是受固有的非线性生产机制影响。尽管随之而来的数学挑战也随之增加，而且显然缺乏有利的结构特性，这也使得此类经典的Keller-Segel模型可用于抛物线爆炸分析等各种技术，本研究试图开发一种能够在这种形式的复杂模型中检测出租车驱动的聚集现象的方法。在相关诺伊曼型初始边值问题的径向对称解的框架内，通过分析相应的质量累积函数，可以得出二维或三维球中有限时间爆炸的结果。严格地证实了所考虑的模型描述局部高密度自发出现的潜力，这是从病毒热点形成现象的背景下的实验观察中得知的。通过分析相应的质量累积函数，可以得出二维或三维球中有限时间爆炸的结果。严格地证实了所考虑的模型描述局部高密度自发出现的潜力，这是从病毒热点形成现象的背景下的实验观察中得知的。通过分析相应的质量累积函数，可以得出二维或三维球中有限时间爆炸的结果。严格地证实了所考虑的模型描述局部高密度自发出现的潜力，这是从病毒热点形成现象的背景下的实验观察中得知的。