On a cross-diffusive SIS epidemic model with power-like nonlinear incidence

TL;DR

This paper analyzes a cross-diffusive SIS epidemic model with a nonlinear infection mechanism, establishing conditions for global solutions, boundedness, and long-term behavior, thereby extending previous research in epidemic modeling.

Contribution

It introduces a generalized nonlinear infection mechanism in a cross-diffusive SIS model and provides new results on global existence, boundedness, and asymptotic behavior of solutions.

Findings

Global existence and boundedness are proven under certain parameters.

Long-term behavior of solutions is characterized as threshold or non-threshold.

The results extend previous studies on epidemic models with nonlinear infection mechanisms.

Abstract

In this work, we study global existence, boundedness and convergence of nonnegative classical solutions of a Neumann initial-boundary value problem for a cross diffusive SIS (susceptible-infected-susceptible) epidemic model with power-like infection mechanism generalizing the standard mass action mechanism. Global existence and boundedness of classical solutions are established in certain parameter ranges, and threshold/non-threshold long-time behaviors of global bounded solutions are also detected. Our findings significantly improve and extend previous related studies.