A reaction-diffusion HFMD model with nonsmooth treatment function

Advances in Difference Equations

article

Shi, Lei¹  Zhao, Hongyong¹  Wu, Daiyong¹ 

[1] Department of Mathematics, Nanjing University of Aeronautics and Astronautics;Department of Mathematics, Guilin University of Technology;Department of Mathematics, Honghe University;Department of Mathematics, Anqing Normal University

关键词: HFMD model;    Nonsmooth treatment;    Basic reproduction number;    Stability analysis;   

DOI  :  10.1186/s13662-021-03294-z

学科分类：航空航天科学

来源: SpringerOpen

【 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.

【 授权许可】

CC BY