Dynamics of a diffusive age-structured HBV model with saturating incidence
In this paper, we propose and investigate an age-structured hepatitis B virus (HBV) model with saturating incidence and spatial diffusion where the viral contamination process is described by the age-since-infection. We first analyze the well-posedness of the initial-boundary values problem of the m...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2016-06-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016024 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590078190288896 |
|---|---|
| author | Xichao Duan Sanling Yuan Kaifa Wang |
| author_facet | Xichao Duan Sanling Yuan Kaifa Wang |
| author_sort | Xichao Duan |
| collection | DOAJ |
| description | In this paper, we propose and investigate an age-structured hepatitis B virus (HBV) model with saturating incidence and spatial diffusion where the viral contamination process is described by the age-since-infection. We first analyze the well-posedness of the initial-boundary values problem of the model in the bounded domain $\Omega\subset\mathbb{R}^n$ and obtain an explicit formula for the basic reproductive number $R_0$ of the model. Then we investigate the global behavior of the model in terms of $R_0$: if $R_0\leq1$, then the uninfected steady state is globally asymptotically stable, whereas if $R_0>1$, then the infected steady state is globally asymptotically stable. In addition, when $R_0>1$, by constructing a suitable Lyapunov-like functional decreasing along the travelling waves to show their convergence towards two steady states as $t$ tends to $\pm\infty$, we prove the existence of traveling wave solutions. Numerical simulations are provided to illustrate the theoretical results. |
| format | Article |
| id | doaj-art-c8707abb1be84cb3bf2cee6a4a4a3c90 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c8707abb1be84cb3bf2cee6a4a4a3c902025-01-24T02:36:57ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-06-0113593596810.3934/mbe.2016024Dynamics of a diffusive age-structured HBV model with saturating incidenceXichao Duan0Sanling Yuan1Kaifa Wang2School of Management, University of Shanghai for Science and Technology, Shanghai 200093College of Science, Shanghai University for Science and Technology, Shanghai 200093Department of Mathematics, School of Biomedical Engineering, Third Military Medical University, Chongqing 400038In this paper, we propose and investigate an age-structured hepatitis B virus (HBV) model with saturating incidence and spatial diffusion where the viral contamination process is described by the age-since-infection. We first analyze the well-posedness of the initial-boundary values problem of the model in the bounded domain $\Omega\subset\mathbb{R}^n$ and obtain an explicit formula for the basic reproductive number $R_0$ of the model. Then we investigate the global behavior of the model in terms of $R_0$: if $R_0\leq1$, then the uninfected steady state is globally asymptotically stable, whereas if $R_0>1$, then the infected steady state is globally asymptotically stable. In addition, when $R_0>1$, by constructing a suitable Lyapunov-like functional decreasing along the travelling waves to show their convergence towards two steady states as $t$ tends to $\pm\infty$, we prove the existence of traveling wave solutions. Numerical simulations are provided to illustrate the theoretical results.https://www.aimspress.com/article/doi/10.3934/mbe.2016024travelling wave solutions.spatial diffusionbasic reproductive numberglobal stabilityage-structured hbv model |
| spellingShingle | Xichao Duan Sanling Yuan Kaifa Wang Dynamics of a diffusive age-structured HBV model with saturating incidence Mathematical Biosciences and Engineering travelling wave solutions. spatial diffusion basic reproductive number global stability age-structured hbv model |
| title | Dynamics of a diffusive age-structured HBV model with saturating incidence |
| title_full | Dynamics of a diffusive age-structured HBV model with saturating incidence |
| title_fullStr | Dynamics of a diffusive age-structured HBV model with saturating incidence |
| title_full_unstemmed | Dynamics of a diffusive age-structured HBV model with saturating incidence |
| title_short | Dynamics of a diffusive age-structured HBV model with saturating incidence |
| title_sort | dynamics of a diffusive age structured hbv model with saturating incidence |
| topic | travelling wave solutions. spatial diffusion basic reproductive number global stability age-structured hbv model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016024 |
| work_keys_str_mv | AT xichaoduan dynamicsofadiffusiveagestructuredhbvmodelwithsaturatingincidence AT sanlingyuan dynamicsofadiffusiveagestructuredhbvmodelwithsaturatingincidence AT kaifawang dynamicsofadiffusiveagestructuredhbvmodelwithsaturatingincidence |