Study of A Delayed SIVA Within-Host Model of Dengue Virus Transmission
During the process of immune response to the infection caused by dengue virus, antibodies are generated by plasma cells which are produced by B-cells. In some cases, it is observed that there is a delay in the production of plasma cells from B-cells which causes a delay in the immune response. We pr...
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| Format: | Article |
| Language: | English |
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Indonesian Bio-Mathematical Society
2023-01-01
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| Series: | Communication in Biomathematical Sciences |
| Subjects: | |
| Online Access: | https://journals.itb.ac.id/index.php/cbms/article/view/19021 |
| _version_ | 1797244986786316288 |
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| author | P. Muthu Bikash Modak |
| author_facet | P. Muthu Bikash Modak |
| author_sort | P. Muthu |
| collection | DOAJ |
| description | During the process of immune response to the infection caused by dengue virus, antibodies are generated by plasma cells which are produced by B-cells. In some cases, it is observed that there is a delay in the production of plasma cells from B-cells which causes a delay in the immune response. We propose a SIVA within-host model of the virus transmission with delayed immune response to articulate the dynamics of the cell and virus population. The stability analysis of different equilibrium states is also studied. The basic reproduction number (BRN) of the model is computed using next generation matrix (NGM) method. The local stability analysis is discussed using the method of linearisation. The stability conditions of the equilibrium states are validated using the Li´enard - Chipart criterion. Hopf bifurcation analysis is carried out as the system has time lag in the immune response. Three equilibrium states, namely, virus free equilibrium state, endemic equilibrium state with and without immune response, have been observed. It has been found that the virus free equilibrium state is locally asymptotically stable if BRN is less than or equal to 1. Additionally, the conditions for the stability of the endemic equilibrium points are derived and elaborated. Numerical simulations for different values of time delay parameter τ are presented and illustrated using graphs. A Hopf bifurcation is observed if the delay parameter τ crosses a threshold value and then the system becomes unstable with periodic solution. To determine the relative importance of the model parameters to the virus transmission and prevalence, sensitivity analysis of the parameters is illustrated using graphs. Due to the time lag in the immune response, an increase in the virus growth is observed in large quantity. As a result, the infection spreads more quickly within the host. |
| first_indexed | 2024-04-24T19:19:44Z |
| format | Article |
| id | doaj.art-7cb5dc24cee243ad878454bc74d8460b |
| institution | Directory Open Access Journal |
| issn | 2549-2896 |
| language | English |
| last_indexed | 2024-04-24T19:19:44Z |
| publishDate | 2023-01-01 |
| publisher | Indonesian Bio-Mathematical Society |
| record_format | Article |
| series | Communication in Biomathematical Sciences |
| spelling | doaj.art-7cb5dc24cee243ad878454bc74d8460b2024-03-26T01:29:13ZengIndonesian Bio-Mathematical SocietyCommunication in Biomathematical Sciences2549-28962023-01-015210112010.5614/cbms.2022.5.2.119613Study of A Delayed SIVA Within-Host Model of Dengue Virus TransmissionP. Muthu0Bikash Modak1Department of Mathematics, National Institute of Technology, Warangal 506004, Telangana, IndiaDepartment of Mathematics, National Institute of Technology, Warangal 506004, Telangana, IndiaDuring the process of immune response to the infection caused by dengue virus, antibodies are generated by plasma cells which are produced by B-cells. In some cases, it is observed that there is a delay in the production of plasma cells from B-cells which causes a delay in the immune response. We propose a SIVA within-host model of the virus transmission with delayed immune response to articulate the dynamics of the cell and virus population. The stability analysis of different equilibrium states is also studied. The basic reproduction number (BRN) of the model is computed using next generation matrix (NGM) method. The local stability analysis is discussed using the method of linearisation. The stability conditions of the equilibrium states are validated using the Li´enard - Chipart criterion. Hopf bifurcation analysis is carried out as the system has time lag in the immune response. Three equilibrium states, namely, virus free equilibrium state, endemic equilibrium state with and without immune response, have been observed. It has been found that the virus free equilibrium state is locally asymptotically stable if BRN is less than or equal to 1. Additionally, the conditions for the stability of the endemic equilibrium points are derived and elaborated. Numerical simulations for different values of time delay parameter τ are presented and illustrated using graphs. A Hopf bifurcation is observed if the delay parameter τ crosses a threshold value and then the system becomes unstable with periodic solution. To determine the relative importance of the model parameters to the virus transmission and prevalence, sensitivity analysis of the parameters is illustrated using graphs. Due to the time lag in the immune response, an increase in the virus growth is observed in large quantity. As a result, the infection spreads more quickly within the host.https://journals.itb.ac.id/index.php/cbms/article/view/19021immune response; time delay; hopf bifurcation |
| spellingShingle | P. Muthu Bikash Modak Study of A Delayed SIVA Within-Host Model of Dengue Virus Transmission Communication in Biomathematical Sciences immune response; time delay; hopf bifurcation |
| title | Study of A Delayed SIVA Within-Host Model of Dengue Virus Transmission |
| title_full | Study of A Delayed SIVA Within-Host Model of Dengue Virus Transmission |
| title_fullStr | Study of A Delayed SIVA Within-Host Model of Dengue Virus Transmission |
| title_full_unstemmed | Study of A Delayed SIVA Within-Host Model of Dengue Virus Transmission |
| title_short | Study of A Delayed SIVA Within-Host Model of Dengue Virus Transmission |
| title_sort | study of a delayed siva within host model of dengue virus transmission |
| topic | immune response; time delay; hopf bifurcation |
| url | https://journals.itb.ac.id/index.php/cbms/article/view/19021 |
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