Proceedings of the
The Nineteenth International Conference on Computational Intelligence and Security (CIS 2023)
December 1 – 4, 2023, Haikou, China
Stability Analysis and Application of a New HIV Infection Model with CTL Response
1Beijing Institute of Control & Electronic Technology, Beijing, China.
2University of Science and Technology Beijing, Beijing, China /EADDRESS/3School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China.
ABSTRACT
Based on the HIV-infected Berlin Patient's clinical data, this study proposes a new anti-human immunodeficiency virus (HIV) infection treatment dynamics model. The model includes four variables: the counts of uninfected CD4+ T cells, infected CD4+ T cells, the load of HIV, and the counts of cytotoxic T lymphocyte (CTL). This model has two equilibrium points: an infection-free state (equilibrium point) and an endemic infection state (equilibrium point). The basic reproductive number R0 of the model is independent of the number of the total CD4+ T cells. However previous models on HIV (anti-HIV) infection (treatment) dynamics have R0 values that depend on the number of CD4+ T cells. Therefore, the biological meanings of those models are questionable. By using Lyapunov functions and LaSalle's invariance principle, it is shown that if our model's R0 is less than one, the infection-free equilibrium point is globally asymptotically stable; if model's R0 is greater than one, the endemic infection equilibrium point is globally asymptotically stable. The proposed model is used to simulate and interpret the dynamics of Berlin Patient's stem cell transplantation and anti-HIV infection treatment.
Keywords: Stemcell transplantation, HIV infectionmodel, Basic reproductive number, Globally asymptotically stable.
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1Beijing Institute of Control & Electronic Technology, Beijing, China.
2University of Science and Technology Beijing, Beijing, China /EADDRESS/3School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China.
ABSTRACT
Based on the HIV-infected Berlin Patient's clinical data, this study proposes a new anti-human immunodeficiency virus (HIV) infection treatment dynamics model. The model includes four variables: the counts of uninfected CD4+ T cells, infected CD4+ T cells, the load of HIV, and the counts of cytotoxic T lymphocyte (CTL). This model has two equilibrium points: an infection-free state (equilibrium point) and an endemic infection state (equilibrium point). The basic reproductive number R0 of the model is independent of the number of the total CD4+ T cells. However previous models on HIV (anti-HIV) infection (treatment) dynamics have R0 values that depend on the number of CD4+ T cells. Therefore, the biological meanings of those models are questionable. By using Lyapunov functions and LaSalle's invariance principle, it is shown that if our model's R0 is less than one, the infection-free equilibrium point is globally asymptotically stable; if model's R0 is greater than one, the endemic infection equilibrium point is globally asymptotically stable. The proposed model is used to simulate and interpret the dynamics of Berlin Patient's stem cell transplantation and anti-HIV infection treatment.
Keywords: Stemcell transplantation, HIV infectionmodel, Basic reproductive number, Globally asymptotically stable.
Download PDF