A reaction-diffusion HFMD model with nonsmooth treatment function
Abstract 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 cert...
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Online Access: | https://doi.org/10.1186/s13662-021-03294-z |
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doaj-1bf5f898960c4a8ebbc99e86a90bf53b2021-03-11T12:41:24ZengSpringerOpenAdvances in Difference Equations1687-18472021-02-012021111910.1186/s13662-021-03294-zA reaction-diffusion HFMD model with nonsmooth treatment functionLei Shi0Hongyong Zhao1Daiyong Wu2Department of Mathematics, Nanjing University of Aeronautics and AstronauticsDepartment of Mathematics, Nanjing University of Aeronautics and AstronauticsDepartment of Mathematics, Nanjing University of Aeronautics and AstronauticsAbstract 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 $R_{0}$ , we use Lyapunov theory to prove that the disease-free equilibrium is globally asymptotically stable as R 0 < 1 $R_{0}<1$ , and the positive equilibrium is globally asymptotically stable as R 0 > 1 $R_{0}>1$ . 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.https://doi.org/10.1186/s13662-021-03294-zHFMD modelNonsmooth treatmentBasic reproduction numberStability analysis |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Lei Shi Hongyong Zhao Daiyong Wu |
spellingShingle |
Lei Shi Hongyong Zhao Daiyong Wu A reaction-diffusion HFMD model with nonsmooth treatment function Advances in Difference Equations HFMD model Nonsmooth treatment Basic reproduction number Stability analysis |
author_facet |
Lei Shi Hongyong Zhao Daiyong Wu |
author_sort |
Lei Shi |
title |
A reaction-diffusion HFMD model with nonsmooth treatment function |
title_short |
A reaction-diffusion HFMD model with nonsmooth treatment function |
title_full |
A reaction-diffusion HFMD model with nonsmooth treatment function |
title_fullStr |
A reaction-diffusion HFMD model with nonsmooth treatment function |
title_full_unstemmed |
A reaction-diffusion HFMD model with nonsmooth treatment function |
title_sort |
reaction-diffusion hfmd model with nonsmooth treatment function |
publisher |
SpringerOpen |
series |
Advances in Difference Equations |
issn |
1687-1847 |
publishDate |
2021-02-01 |
description |
Abstract 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 $R_{0}$ , we use Lyapunov theory to prove that the disease-free equilibrium is globally asymptotically stable as R 0 < 1 $R_{0}<1$ , and the positive equilibrium is globally asymptotically stable as R 0 > 1 $R_{0}>1$ . 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. |
topic |
HFMD model Nonsmooth treatment Basic reproduction number Stability analysis |
url |
https://doi.org/10.1186/s13662-021-03294-z |
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