Threshold dynamics of a nonlocal dispersal SIS epidemic model with free boundaries

TL;DR

This paper investigates how the movement of infection boundaries and spatial factors influence disease spread in a nonlocal SIS epidemic model, highlighting the roles of media, healthcare, and diffusion types.

Contribution

It introduces a nonlocal SIS model with free boundaries, analyzes the principal eigenvalue, and derives conditions for disease spreading or vanishing, emphasizing the effects of media and healthcare.

Findings

Large media coverage and hospital beds help control disease.

Nonlocal diffusion allows more diverse spreading scenarios.

Eigenvalue analysis predicts disease outcomes based on parameters.

Abstract

To study the influence of the moving front of the infected interval and the spatial movement of individuals on the spreading or vanishing of infectious disease, we consider a nonlocal SIS (susceptible-infected-susceptible) reaction-diffusion model with media coverage, hospital bed numbers and free boundaries. The principal eigenvalue of the integral operator is defined, and the impacts of the diffusion rate of infected individuals and interval length on the principal eigenvalue are analyzed. Furthermore, sufficient conditions for spreading and vanishing of the disease are derived.Our results show that large media coverage and hospital bed numbers are beneficial to the prevention and control of disease. The difference between the model with nonlocal diffusion and that with local diffusion is also discussed and nonlocal diffusion leads to more possibilities.