Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission

Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission

In this paper, we focus on spreading speed of a reaction-diffusion SI epidemic model with vertical transmission, which is a non-monotone system. More specifically, we prove that the solution of the system converges to the disease-free equilibrium as $ t \rightarrow \infty $ if $ R_{0} \leqslant 1 $...

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Autores principales: Lin Zhao, Haifeng Huo
Formato: article
Lenguaje:EN
Publicado: AIMS Press 2021
Materias:
non-monotone system
si epidemic model
vertical transmission
spreading speed
Biotechnology
TP248.13-248.65
Mathematics
QA1-939
Acceso en línea:https://doaj.org/article/ab9bb6e4d2f4488299bbbf6372fa8d32
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spelling oai:doaj.org-article:ab9bb6e4d2f4488299bbbf6372fa8d322021-11-11T00:51:56ZSpatial propagation for a reaction-diffusion SI epidemic model with vertical transmission10.3934/mbe.20213011551-0018https://doaj.org/article/ab9bb6e4d2f4488299bbbf6372fa8d322021-07-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021301?viewType=HTMLhttps://doaj.org/toc/1551-0018In this paper, we focus on spreading speed of a reaction-diffusion SI epidemic model with vertical transmission, which is a non-monotone system. More specifically, we prove that the solution of the system converges to the disease-free equilibrium as $ t \rightarrow \infty $ if $ R_{0} \leqslant 1 $ and if $ R_0 > 1 $, there exists a critical speed $ c^\diamond > 0 $ such that if $ \|x\| = ct $ with $ c \in (0, c^\diamond) $, the disease is persistent and if $ \|x\| \geqslant ct $ with $ c > c^\diamond $, the infection dies out. Finally, we illustrate the asymptotic behaviour of the solution of the system via numerical simulations.Lin Zhao Haifeng HuoAIMS Pressarticlenon-monotone systemsi epidemic modelvertical transmissionspreading speedBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 6012-6033 (2021)
institution DOAJ
collection DOAJ
language EN
topic non-monotone system
si epidemic model
vertical transmission
spreading speed
Biotechnology
TP248.13-248.65
Mathematics
QA1-939
spellingShingle non-monotone system
si epidemic model
vertical transmission
spreading speed
Biotechnology
TP248.13-248.65
Mathematics
QA1-939
Lin Zhao
Haifeng Huo
Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission
description In this paper, we focus on spreading speed of a reaction-diffusion SI epidemic model with vertical transmission, which is a non-monotone system. More specifically, we prove that the solution of the system converges to the disease-free equilibrium as $ t \rightarrow \infty $ if $ R_{0} \leqslant 1 $ and if $ R_0 > 1 $, there exists a critical speed $ c^\diamond > 0 $ such that if $ \|x\| = ct $ with $ c \in (0, c^\diamond) $, the disease is persistent and if $ \|x\| \geqslant ct $ with $ c > c^\diamond $, the infection dies out. Finally, we illustrate the asymptotic behaviour of the solution of the system via numerical simulations.
format article
author Lin Zhao
Haifeng Huo
author_facet Lin Zhao
Haifeng Huo
author_sort Lin Zhao
title Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission
title_short Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission
title_full Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission
title_fullStr Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission
title_full_unstemmed Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission
title_sort spatial propagation for a reaction-diffusion si epidemic model with vertical transmission
publisher AIMS Press
publishDate 2021
url https://doaj.org/article/ab9bb6e4d2f4488299bbbf6372fa8d32
work_keys_str_mv AT linzhao spatialpropagationforareactiondiffusionsiepidemicmodelwithverticaltransmission
AT haifenghuo spatialpropagationforareactiondiffusionsiepidemicmodelwithverticaltransmission
_version_ 1718439613431808000

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