Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities
Youshan Tao, Michael Winkler, Institut für Mathematik, Universität Paderborn, 33098 Paderborn, Germany
Abstract
This manuscript is concerned with the homogeneous Neumann initial-boundary problem for a susceptible-infected-susceptible model involving chemotactic movement of susceptibles away from infected individuals, as well as a mass action infection mechanism in its full quadratic strength. By constructing a quasi-energy functional on the basis of a suitable exploitation of a zero-order dissipative term together with the impact of diffusion, under an assumption on asymptotic smallness of the prescribed tactic sensitivity at large cell-densities a result on global existence of classical solutions emanating from initial data of arbitrary size is derived.