Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects
We propose and study a viral infection model with two nonlocal effects and a general incidence rate. First, the semigroup theory and the classical renewal process are adopted to compute the basic reproduction number R0 as the spectral radius of the next-generation operator. It is shown that R0 equal...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/5842942 |
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| _version_ | 1832545821321592832 |
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| author | Xiaoyan Wang Yuming Chen Junyuan Yang |
| author_facet | Xiaoyan Wang Yuming Chen Junyuan Yang |
| author_sort | Xiaoyan Wang |
| collection | DOAJ |
| description | We propose and study a viral infection model with two nonlocal effects and a general incidence rate. First, the semigroup theory and the classical renewal process are adopted to compute the basic reproduction number R0 as the spectral radius of the next-generation operator. It is shown that R0 equals the principal eigenvalue of a linear operator associated with a positive eigenfunction. Then we obtain the existence of endemic steady states by Shauder fixed point theorem. A threshold dynamics is established by the approach of Lyapunov functionals. Roughly speaking, if R0<1, then the virus-free steady state is globally asymptotically stable; if R0>1, then the endemic steady state is globally attractive under some additional conditions on the incidence rate. Finally, the theoretical results are illustrated by numerical simulations based on a backward Euler method. |
| format | Article |
| id | doaj-art-eb66b3eda40c49059f00c51bffe3cb85 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-eb66b3eda40c49059f00c51bffe3cb852025-02-03T07:24:45ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/58429425842942Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal EffectsXiaoyan Wang0Yuming Chen1Junyuan Yang2School of Information Management, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030051, ChinaDepartment of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, CanadaComplex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, ChinaWe propose and study a viral infection model with two nonlocal effects and a general incidence rate. First, the semigroup theory and the classical renewal process are adopted to compute the basic reproduction number R0 as the spectral radius of the next-generation operator. It is shown that R0 equals the principal eigenvalue of a linear operator associated with a positive eigenfunction. Then we obtain the existence of endemic steady states by Shauder fixed point theorem. A threshold dynamics is established by the approach of Lyapunov functionals. Roughly speaking, if R0<1, then the virus-free steady state is globally asymptotically stable; if R0>1, then the endemic steady state is globally attractive under some additional conditions on the incidence rate. Finally, the theoretical results are illustrated by numerical simulations based on a backward Euler method.http://dx.doi.org/10.1155/2019/5842942 |
| spellingShingle | Xiaoyan Wang Yuming Chen Junyuan Yang Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects Complexity |
| title | Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects |
| title_full | Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects |
| title_fullStr | Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects |
| title_full_unstemmed | Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects |
| title_short | Spatial and Temporal Dynamics of a Viral Infection Model with Two Nonlocal Effects |
| title_sort | spatial and temporal dynamics of a viral infection model with two nonlocal effects |
| url | http://dx.doi.org/10.1155/2019/5842942 |
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