Modeling the Adaptive Immune Response in an HBV Infection Model with Virus to Cell Transmission in Both Liver with CTL Immune Response and the Extrahepatic Tissue
The objective of this paper is to investigate a mathematical model describing the infection of hepatitis B virus (HBV) in intrahepatic and extrahepatic tissues. Additionally, the model includes the effect of the cytotoxic T cell (CTL) immunity, which is described by a linear activation rate by infec...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/27/4/65 |
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| author | Fatima Ezzahra Fikri Karam Allali |
| author_facet | Fatima Ezzahra Fikri Karam Allali |
| author_sort | Fatima Ezzahra Fikri |
| collection | DOAJ |
| description | The objective of this paper is to investigate a mathematical model describing the infection of hepatitis B virus (HBV) in intrahepatic and extrahepatic tissues. Additionally, the model includes the effect of the cytotoxic T cell (CTL) immunity, which is described by a linear activation rate by infected cells. The positivity and boundedness of solutions for non-negative initial data are proven, which is consistent with the biological studies. The local stability of the equilibrium is established. In addition to this, the global stability of the disease-free equilibrium and the endemic equilibrium is fulfilled by using appropriate Lyapanov functions. Finally, numerical simulations are performed to support our theoretical findings. It has been revealed that the fractional-order derivatives have no influence on the stability but only on the speed of convergence toward the equilibria. |
| first_indexed | 2024-03-09T09:52:51Z |
| format | Article |
| id | doaj.art-63118083fb6e4791981bde1d20beb784 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-09T09:52:51Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-63118083fb6e4791981bde1d20beb7842023-12-01T23:58:17ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472022-07-012746510.3390/mca27040065Modeling the Adaptive Immune Response in an HBV Infection Model with Virus to Cell Transmission in Both Liver with CTL Immune Response and the Extrahepatic TissueFatima Ezzahra Fikri0Karam Allali1Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O. Box 146, Mohammedia 20650, MoroccoLaboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O. Box 146, Mohammedia 20650, MoroccoThe objective of this paper is to investigate a mathematical model describing the infection of hepatitis B virus (HBV) in intrahepatic and extrahepatic tissues. Additionally, the model includes the effect of the cytotoxic T cell (CTL) immunity, which is described by a linear activation rate by infected cells. The positivity and boundedness of solutions for non-negative initial data are proven, which is consistent with the biological studies. The local stability of the equilibrium is established. In addition to this, the global stability of the disease-free equilibrium and the endemic equilibrium is fulfilled by using appropriate Lyapanov functions. Finally, numerical simulations are performed to support our theoretical findings. It has been revealed that the fractional-order derivatives have no influence on the stability but only on the speed of convergence toward the equilibria.https://www.mdpi.com/2297-8747/27/4/65adaptive immune responsecompartmentCTL immune responsesfractional order modelHBV infectionintrahepatic compartment |
| spellingShingle | Fatima Ezzahra Fikri Karam Allali Modeling the Adaptive Immune Response in an HBV Infection Model with Virus to Cell Transmission in Both Liver with CTL Immune Response and the Extrahepatic Tissue Mathematical and Computational Applications adaptive immune response compartment CTL immune responses fractional order model HBV infection intrahepatic compartment |
| title | Modeling the Adaptive Immune Response in an HBV Infection Model with Virus to Cell Transmission in Both Liver with CTL Immune Response and the Extrahepatic Tissue |
| title_full | Modeling the Adaptive Immune Response in an HBV Infection Model with Virus to Cell Transmission in Both Liver with CTL Immune Response and the Extrahepatic Tissue |
| title_fullStr | Modeling the Adaptive Immune Response in an HBV Infection Model with Virus to Cell Transmission in Both Liver with CTL Immune Response and the Extrahepatic Tissue |
| title_full_unstemmed | Modeling the Adaptive Immune Response in an HBV Infection Model with Virus to Cell Transmission in Both Liver with CTL Immune Response and the Extrahepatic Tissue |
| title_short | Modeling the Adaptive Immune Response in an HBV Infection Model with Virus to Cell Transmission in Both Liver with CTL Immune Response and the Extrahepatic Tissue |
| title_sort | modeling the adaptive immune response in an hbv infection model with virus to cell transmission in both liver with ctl immune response and the extrahepatic tissue |
| topic | adaptive immune response compartment CTL immune responses fractional order model HBV infection intrahepatic compartment |
| url | https://www.mdpi.com/2297-8747/27/4/65 |
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