A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus
In this paper, we will consider three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of these three models based on dynamical sys...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/8/1594 |
| _version_ | 1797407777569636352 |
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| author | Florian Munteanu |
| author_facet | Florian Munteanu |
| author_sort | Florian Munteanu |
| collection | DOAJ |
| description | In this paper, we will consider three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of these three models based on dynamical systems theory will be performed by studying the local behavior of the equilibrium points and obtaining the local dynamics properties from the linear stability point of view. Additionally, we will compare these models in order to understand which is more appropriate to model the interaction between the human immune system and a virus. Some natural medical interpretations will be obtained, which are available for all three models and can be useful to the medical community. |
| first_indexed | 2024-03-09T03:46:34Z |
| format | Article |
| id | doaj.art-8d10b419417f4699a9bbb18cda43b6af |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T03:46:34Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8d10b419417f4699a9bbb18cda43b6af2023-12-03T14:33:02ZengMDPI AGSymmetry2073-89942022-08-01148159410.3390/sym14081594A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a VirusFlorian Munteanu0Department of Applied Mathematics, University of Craiova, Al. I. Cuza, 13, 200585 Craiova, RomaniaIn this paper, we will consider three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of these three models based on dynamical systems theory will be performed by studying the local behavior of the equilibrium points and obtaining the local dynamics properties from the linear stability point of view. Additionally, we will compare these models in order to understand which is more appropriate to model the interaction between the human immune system and a virus. Some natural medical interpretations will be obtained, which are available for all three models and can be useful to the medical community.https://www.mdpi.com/2073-8994/14/8/1594mathematical modelssystems of ordinary differential equationsdynamical systemsstability |
| spellingShingle | Florian Munteanu A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus Symmetry mathematical models systems of ordinary differential equations dynamical systems stability |
| title | A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus |
| title_full | A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus |
| title_fullStr | A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus |
| title_full_unstemmed | A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus |
| title_short | A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus |
| title_sort | comparative study of three mathematical models for the interaction between the human immune system and a virus |
| topic | mathematical models systems of ordinary differential equations dynamical systems stability |
| url | https://www.mdpi.com/2073-8994/14/8/1594 |
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