Analysis of a chemotaxis-SIS epidemic model with unbounded infection force. (June 2023) - Tao, Youshan; Winkler, Michael
Abstract: A susceptible–infected–susceptible (SIS) model is considered which includes both taxis type cross-diffusive motion of susceptibles and a mass action infection mechanism. An associated no-flux initial–boundary value problem in one-dimensional bounded intervals is shown to admit globally bounded classical solutions for initial data of arbitrary size. For a higher-dimensional counterpart, a result on global classical solvability in the presence of suitably small initial data is derived. This is complemented by a statement on large time stabilization of small-data trajectories toward spatially constant and infection-free equilibria under an assumption on strict positivity of the considered space-dependent recovery rate.