Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence
In this paper, a discrete-time model has been proposed by applying nonstandard finite difference (NSFD) scheme to solve a delayed viral infection model with immune response and general nonlinear incidence. It is shown that the discrete model has equilibria which are exactly the same as those of the...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/3141736 |
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| _version_ | 1849412540837134336 |
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| author | Jinhu Xu Yan Geng |
| author_facet | Jinhu Xu Yan Geng |
| author_sort | Jinhu Xu |
| collection | DOAJ |
| description | In this paper, a discrete-time model has been proposed by applying nonstandard finite difference (NSFD) scheme to solve a delayed viral infection model with immune response and general nonlinear incidence. It is shown that the discrete model has equilibria which are exactly the same as those of the original continuous model. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria of the discrete model is fully determined by the basic reproduction number of the virus and immune response, R0 and R1, with no restriction on the time step size, which implies that the NSFD scheme preserves the qualitative dynamics of the corresponding continuous model. |
| format | Article |
| id | doaj-art-63fb617bb6e94240b3aa0c5ccc0d76a3 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-63fb617bb6e94240b3aa0c5ccc0d76a32025-08-20T03:34:25ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/31417363141736Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear IncidenceJinhu Xu0Yan Geng1Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaIn this paper, a discrete-time model has been proposed by applying nonstandard finite difference (NSFD) scheme to solve a delayed viral infection model with immune response and general nonlinear incidence. It is shown that the discrete model has equilibria which are exactly the same as those of the original continuous model. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria of the discrete model is fully determined by the basic reproduction number of the virus and immune response, R0 and R1, with no restriction on the time step size, which implies that the NSFD scheme preserves the qualitative dynamics of the corresponding continuous model.http://dx.doi.org/10.1155/2017/3141736 |
| spellingShingle | Jinhu Xu Yan Geng Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence Discrete Dynamics in Nature and Society |
| title | Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence |
| title_full | Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence |
| title_fullStr | Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence |
| title_full_unstemmed | Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence |
| title_short | Dynamic Consistent NSFD Scheme for a Delayed Viral Infection Model with Immune Response and Nonlinear Incidence |
| title_sort | dynamic consistent nsfd scheme for a delayed viral infection model with immune response and nonlinear incidence |
| url | http://dx.doi.org/10.1155/2017/3141736 |
| work_keys_str_mv | AT jinhuxu dynamicconsistentnsfdschemeforadelayedviralinfectionmodelwithimmuneresponseandnonlinearincidence AT yangeng dynamicconsistentnsfdschemeforadelayedviralinfectionmodelwithimmuneresponseandnonlinearincidence |