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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| Format: | Article |
| Language: | English |
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AIMS Press
2021-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2021301?viewType=HTML |
| _version_ | 1818986901238972416 |
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| author | Lin Zhao Haifeng Huo |
| author_facet | Lin Zhao Haifeng Huo |
| author_sort | Lin Zhao |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-20T18:58:09Z |
| format | Article |
| id | doaj.art-ab9bb6e4d2f4488299bbbf6372fa8d32 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-20T18:58:09Z |
| publishDate | 2021-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-ab9bb6e4d2f4488299bbbf6372fa8d322022-12-21T19:29:28ZengAIMS PressMathematical Biosciences and Engineering1551-00182021-07-011856012603310.3934/mbe.2021301Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmissionLin Zhao 0Haifeng Huo1Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, ChinaIn 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.https://www.aimspress.com/article/doi/10.3934/mbe.2021301?viewType=HTMLnon-monotone systemsi epidemic modelvertical transmissionspreading speed |
| spellingShingle | Lin Zhao Haifeng Huo Spatial propagation for a reaction-diffusion SI epidemic model with vertical transmission Mathematical Biosciences and Engineering non-monotone system si epidemic model vertical transmission spreading speed |
| title | 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_short | 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 |
| topic | non-monotone system si epidemic model vertical transmission spreading speed |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2021301?viewType=HTML |
| work_keys_str_mv | AT linzhao spatialpropagationforareactiondiffusionsiepidemicmodelwithverticaltransmission AT haifenghuo spatialpropagationforareactiondiffusionsiepidemicmodelwithverticaltransmission |