文章基本信息

标题：A reaction-diffusion HFMD model with nonsmooth treatment function
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作者：Lei Shi ; Hongyong Zhao ; Daiyong Wu 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2021
卷号：2021
期号：1
页码：1
DOI：10.1186/s13662-021-03294-z
出版社：Hindawi Publishing Corporation
摘要：Hand, foot, and mouth disease (HFMD) is a contagious viral illness that commonly affects infants and children. In some areas with high incidence of this disease, the relevant departments often use some strategies to strengthen treatment when the number of infected individuals exceeds a certain threshold. To assess the effectiveness of strengthening treatment strategies which depend on a certain threshold, we propose a new reaction-diffusion model with nonsmooth treatment function to investigate the spread of HFMD. In the case of the spatial domain being bounded, by defining the basic reproduction number $R_{0}$ , we use Lyapunov theory to prove that the disease-free equilibrium is globally asymptotically stable as $R_{0}1$ . In the case of the spatial domain being linear and unbounded, in order to study how the movement of children impacts the spatial spread of HFMD, we further consider the traveling waves. Finally, numerical simulations demonstrate the effectiveness of the theoretical analysis.
关键词：HFMD model ; Nonsmooth treatment ; Basic reproduction number ; Stability analysis