Analysis of a chemotaxis-SIS epidemic model with unbounded infection force (Q6099579)

The SIS model being discussed takes into account both taxis type cross-diffusive motion of susceptibles and a mass action infection mechanism. The model's associated no-flux initial-boundary value problem is shown to have globally bounded classical solutions for initial data of any size within one-dimensional bounded intervals. The higher-dimensional counterpart also has a result on global classical solvability when initial data is suitably small. It is also accompanied by a statement on stabilization of small-data trajectories over a long period towards spatially constant and infection-free equilibria under the assumption of strict positivity of the considered space-dependent recovery rate.