  Partial differential equation (PDE) models for infectious disease have
received renewed interest in recent years. Most models of this type extend
classical compartmental formulations with additional terms accounting for
spatial dynamics, with Fickian diffusion being the most common such term.
However, while diffusion may be appropriate for modeling vector-borne diseases,
or diseases among plants or wildlife, the spatial propagation of airborne
diseases in human populations is heavily dependent on human contact and
mobility patterns, which are not necessarily well-described by diffusion. By
including an additional chemotaxis-inspired term, in which the infection is
propagated along the positive gradient of the susceptible population (from
regions of low- to high-density of susceptibles), one may provide a more
suitable description of these dynamics. This article introduces and analyzes a
mathematical model of infectious disease incorporating a modified
chemotaxis-type term. The model is analyzed mathematically and the
well-posedness of the resulting PDE system is demonstrated. A series of
numerical simulations are provided, demonstrating the ability of the model to
naturally capture important phenomena not easily observed in standard diffusion
models, including propagation over long spatial distances over short time
scales and the emergence of localized infection hotspots
