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Dynamics of a Nonlocal Dispersal Foot-and-Mouth Disease Model in a Spatially Heterogeneous Environment
Acta Mathematica Scientia ( IF 1 ) Pub Date : 2021-01-29 , DOI: 10.1007/s10473-021-0217-y
Xiaoyan Wang , Junyuan Yang

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 \({{\cal R}_0}\) is defined as the spectral radius of the next generation operator \({\cal R}\left( x \right)\) by a renewal equation. The relationship between \({{\cal R}_0}\) and a principal eigenvalue of an operator \({{\cal L}_0}\) is built. Moreover, the proposed system exhibits threshold dynamics in terms of \({{\cal R}_0}\), in the sense that \({{\cal R}_0}\) 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.



中文翻译:

空间非均质环境中非局部弥漫性手足口病模型的动力学

口蹄疫是世界上主要的传染性人畜共患病之一。它是由细小核糖核酸病毒家族的水痘病毒属的各种物种引起的,它总是带来大量的感染和沉重的经济损失。该疾病已成为主要的公共卫生问题。在本文中,我们提出了一种在空间异质性环境中的非局部口蹄疫模型,该模型耦合了病毒到动物和动物到动物的传播途径,并研究了传播的动力学。通过更新方程将基本再现数\({{\ cal R} _0} \定义为下一代算子\ {{calcal} \ left(x \ right)\)的光谱半径。\({{\ cal R} _0} \)之间的关系并建立运算符\({{\ cal L} _0} \)的本征值。此外,从\({{\ cal R} _0} \)确定是否患有口蹄疫的意义上讲,拟议的系统具有\({{\ cal R} _0} \)的阈值动态。入侵主机。通过数值模拟,我们发现增加动物的运动是预防这种疾病流行的有效控制措施。

更新日期:2021-01-29
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