Publication
Discrete-time system of an intracellular delayed HIV model with CTL immune response
| Summary: | In [Math. Comput. Sci. 12 (2018), no. 2, 111–127], a delayed model describing the dynamics of the Human Immunodeficiency Virus (HIV) with Cyto- toxic T Lymphocytes (CTL) immune response is investigated by Allali, Harroudi and Torres. Here, we propose a discrete-time version of that model, which includes four nonlinear difference equations describing the evolution of uninfected, infected, free HIV viruses, and CTL immune response cells and includes intracellular delay. Using suitable Lyapunov functions, we prove the global stability of the disease free equilib- rium point and of the two endemic equilibrium points. We finalize by making some simulations and showing, numerically, the consistence of the obtained theoretical results. |
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| Main Authors: | Vaz, Sandra |
| Other Authors: | Torres, Delfim F. M. |
| Subject: | Compartmental models Stability analysis Lyapunov functions Mickens method |
| Year: | 2022 |
| Country: | Portugal |
| Document type: | book part |
| Access type: | restricted access |
| Associated institution: | Universidade de Aveiro |
| Language: | English |
| Origin: | RIA - Repositório Institucional da Universidade de Aveiro |
| Summary: | In [Math. Comput. Sci. 12 (2018), no. 2, 111–127], a delayed model describing the dynamics of the Human Immunodeficiency Virus (HIV) with Cyto- toxic T Lymphocytes (CTL) immune response is investigated by Allali, Harroudi and Torres. Here, we propose a discrete-time version of that model, which includes four nonlinear difference equations describing the evolution of uninfected, infected, free HIV viruses, and CTL immune response cells and includes intracellular delay. Using suitable Lyapunov functions, we prove the global stability of the disease free equilib- rium point and of the two endemic equilibrium points. We finalize by making some simulations and showing, numerically, the consistence of the obtained theoretical results. |
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