Yachun Tong | Searcharxiv

arXiv2023

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

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.

math.AP↗

arXiv2020

Spatial diffusion and periodic evolving of domain in an SIS epidemic model

In order to explore the impact of periodically evolving domain on the transmission of disease, we study a SIS reaction-diffusion model with logistic term on a periodically evolving domain. The basic reproduction number ${\mathcal{R}}_0$ is given by the next generation infection operator, and relies on the evolving rate of the periodically evolving domain, diffusion coefficient of infected individuals $d_I$ and size of the space. The monotonicity of ${\mathcal{R}}_0$ with respect to $d_I$, evolving rate $ρ(t)$ and interval length $L$ are derived, and asymptotic property of ${\mathcal{R}}_0$ if $d_I$ or $L$ is small enough or large enough in one-dimensional space are discussed. ${\mathcal{R}}_0$ as threshold can be used to characterize whether the disease-free equilibrium is stable or not. Our theoretical results and numerical simulations indicate that small evolving rate, small diffusion of infected individuals and small interval length have positive impact on prevention and control of disease.

math.AP↗