Global dynamics of humoral and cellular immune responses to virus infection
We study the global stability of a model of virus dynamics with consideration of humoral and cellular immune responses. We use a Lyapunov direct method to obtain sufficient conditions for the global s tability of virus-free and viruspresence equilibriums. First, we analyze the model without an imm...
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| Format: | Article |
| Language: | English |
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Pontificia Universidad Javeriana
2019-08-01
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| Series: | Universitas Scientiarum |
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| Online Access: | https://revistas.javeriana.edu.co/index.php/scientarium/article/view/23601 |
| _version_ | 1819039539298041856 |
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| author | Miller Cerón-Gómez, Hyun Mo Yang |
| author_facet | Miller Cerón-Gómez, Hyun Mo Yang |
| author_sort | Miller Cerón-Gómez, Hyun Mo Yang |
| collection | DOAJ |
| description | We study the global stability of a model of virus dynamics with consideration
of humoral and cellular immune responses. We use a Lyapunov direct method
to obtain sufficient conditions for the global s tability of virus-free and viruspresence equilibriums. First, we analyze the model without an immune response
and found that if the reproductive number of the virus is less than or equal to
one, the virus-free equilibrium is globally asymptotically stable. However, for
the virus-presence equilibrium, global stability is obtained if the virus entrance
rate into the target cells is less than one. We analyze the model with humoral and
cellular immune responses and found similar results. The difference is that in the
reproductive number of the virus and in the virus entrance rate into the target
cells appear parameters of humoral and cellular immune responses, which means
that the adaptive immune response will cease or control the rise of the infectionWe study the global stability of a model of virus dynamics with consideration
of humoral and cellular immune responses. We use a Lyapunov direct method
to obtain sufficient conditions for the global s tability of virus-free and viruspresence equilibriums. First, we analyze the model without an immune response
and found that if the reproductive number of the virus is less than or equal to
one, the virus-free equilibrium is globally asymptotically stable. However, for
the virus-presence equilibrium, global stability is obtained if the virus entrance
rate into the target cells is less than one. We analyze the model with humoral and
cellular immune responses and found similar results. The difference is that in the
reproductive number of the virus and in the virus entrance rate into the target
cells appear parameters of humoral and cellular immune responses, which means
that the adaptive immune response will cease or control the rise of the infection. |
| first_indexed | 2024-12-21T08:54:49Z |
| format | Article |
| id | doaj.art-bfb64f36eb974980a297591624bd079f |
| institution | Directory Open Access Journal |
| issn | 0122-7483 2027-1352 |
| language | English |
| last_indexed | 2024-12-21T08:54:49Z |
| publishDate | 2019-08-01 |
| publisher | Pontificia Universidad Javeriana |
| record_format | Article |
| series | Universitas Scientiarum |
| spelling | doaj.art-bfb64f36eb974980a297591624bd079f2022-12-21T19:09:35ZengPontificia Universidad JaverianaUniversitas Scientiarum0122-74832027-13522019-08-0124140742310.11144/Javeriana.SC24-2.gdohGlobal dynamics of humoral and cellular immune responses to virus infectionMiller Cerón-Gómez, Hyun Mo Yang0Universidad de Nariño, Torobajo, Calle 18 Carrera 50, Pasto - Colombia, Universidade Estadual de Campinas, Cidade Universitária “Zeferino Vaz" CEP 13083-970, Campinas - BrasilWe study the global stability of a model of virus dynamics with consideration of humoral and cellular immune responses. We use a Lyapunov direct method to obtain sufficient conditions for the global s tability of virus-free and viruspresence equilibriums. First, we analyze the model without an immune response and found that if the reproductive number of the virus is less than or equal to one, the virus-free equilibrium is globally asymptotically stable. However, for the virus-presence equilibrium, global stability is obtained if the virus entrance rate into the target cells is less than one. We analyze the model with humoral and cellular immune responses and found similar results. The difference is that in the reproductive number of the virus and in the virus entrance rate into the target cells appear parameters of humoral and cellular immune responses, which means that the adaptive immune response will cease or control the rise of the infectionWe study the global stability of a model of virus dynamics with consideration of humoral and cellular immune responses. We use a Lyapunov direct method to obtain sufficient conditions for the global s tability of virus-free and viruspresence equilibriums. First, we analyze the model without an immune response and found that if the reproductive number of the virus is less than or equal to one, the virus-free equilibrium is globally asymptotically stable. However, for the virus-presence equilibrium, global stability is obtained if the virus entrance rate into the target cells is less than one. We analyze the model with humoral and cellular immune responses and found similar results. The difference is that in the reproductive number of the virus and in the virus entrance rate into the target cells appear parameters of humoral and cellular immune responses, which means that the adaptive immune response will cease or control the rise of the infection.https://revistas.javeriana.edu.co/index.php/scientarium/article/view/23601global stability; immune response; lyapunov direct method. |
| spellingShingle | Miller Cerón-Gómez, Hyun Mo Yang Global dynamics of humoral and cellular immune responses to virus infection Universitas Scientiarum global stability; immune response; lyapunov direct method. |
| title | Global dynamics of humoral and cellular immune responses to virus infection |
| title_full | Global dynamics of humoral and cellular immune responses to virus infection |
| title_fullStr | Global dynamics of humoral and cellular immune responses to virus infection |
| title_full_unstemmed | Global dynamics of humoral and cellular immune responses to virus infection |
| title_short | Global dynamics of humoral and cellular immune responses to virus infection |
| title_sort | global dynamics of humoral and cellular immune responses to virus infection |
| topic | global stability; immune response; lyapunov direct method. |
| url | https://revistas.javeriana.edu.co/index.php/scientarium/article/view/23601 |
| work_keys_str_mv | AT millercerongomezhyunmoyang globaldynamicsofhumoralandcellularimmuneresponsestovirusinfection |