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Dynamics of a Nonlocal Dispersal Foot-and-Mouth Disease Model in a Spatially Heterogeneous Environment

Authors
  • Wang, Xiaoyan1
  • Yang, Junyuan2
  • 1 Shanxi University of Finance and Economics, Taiyuan, 030006, China , Taiyuan (China)
  • 2 Shanxi University, Taiyuan, 030006, China , Taiyuan (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jan 29, 2021
Volume
41
Issue
2
Pages
552–572
Identifiers
DOI: 10.1007/s10473-021-0217-y
Source
Springer Nature
Keywords
License
Yellow

Abstract

Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world. It is caused by various species of the genus Aphthovirus of the family Picornavirus, and it always brings a large number of infections and heavy financial losses. The disease has become a major public health concern. In this paper, we propose a nonlocal foot-and-mouth disease model in a spatially heterogeneous environment, which couples virus-to-animals and animals-to-animals transmission pathways, and investigate the dynamics of the disperal. The basic reproduction number ℛ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\cal R}_0}$$\end{document} is defined as the spectral radius of the next generation operator ℛ(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal R}\left( x \right)$$\end{document} by a renewal equation. The relationship between ℛ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\cal R}_0}$$\end{document} and a principal eigenvalue of an operator ℒ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\cal L}_0}$$\end{document} is built. Moreover, the proposed system exhibits threshold dynamics in terms of ℛ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\cal R}_0}$$\end{document}, in the sense that ℛ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\cal R}_0}$$\end{document} determines whether or not foot-and-mouth disease invades the hosts. Through numerical simulations, we have found that increasing animals’ movements is an effective control measure for preventing prevalence of the disease.

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