The free boundary problem of an epidemic model with nonlocal diffusions and nonlocal reactions: spreadingvanishing dichotomy
Abstract
This paper concerns the free boundary problem of an epidemic model. The spatial movements of the infectious agents and the infective humans are approximated by nonlocal diffusion operators. Especially, both the growth rate of the agents and the infective rate of humans are represented by nonlocal reaction terms. Thus our model has four integral terms which bring some diffculties for the study of the corresponding principal eigenvalue problem. Firstly, using some elementray analysis instead of KreinRutman theorem and the variational characteristic, we obtain the existence and asymptotic behaviors of principal eigenvalue. Then a spreadingvanishing dichotomy is proved to hold, and the criteria for spreading and vanishing are derived. Lastly, comparing our results with those in the existing works, we discuss the effect of nonlocal reaction term on spreading and vanishing, finding that the more nonlocal reaction terms a model has, the harder spreading happens.
 Publication:

arXiv eprints
 Pub Date:
 June 2024
 DOI:
 10.48550/arXiv.2406.04880
 arXiv:
 arXiv:2406.04880
 Bibcode:
 2024arXiv240604880L
 Keywords:

 Mathematics  Analysis of PDEs