### Mathematical Biosciences and Engineering

2021, Issue 1:57-68. doi: 10.3934/mbe.2021003
Research article Special Issues

# Global stability of an HIV infection model with saturated CTL immune response and intracellular delay

• Received: 13 September 2020 Accepted: 10 November 2020 Published: 19 November 2020
• In this paper, we consider an HIV infection model with saturated infection rate, intracellular delay and saturated cytotoxic T lymphocyte (CTL) immune response. By calculation, we obtain immunity-inactivated reproduction number $\mathscr{R}_0$ and immunity-activated reproduction number $\mathscr{R}_1$. By analyzing the distribution of roots of the corresponding characteristic equations, we study the local stability of an infection-free equilibrium, an immunity-inactivated equilibrium and an immunity-activated equilibrium of the model. By constructing suitable Lyapunov functionals and using LaSalle's invariance principle, we show that if $\mathscr{R}_0 < 1$, the infection-free equilibrium is globally asymptotically stable; If $\mathscr{R}_1 < 1 < \mathscr{R}_0$, the immunity-inactivated equilibrium is globally asymptotically stable; If $\mathscr{R}_1>1$, the immunity-activated equilibrium is globally asymptotically stable. Sensitivity analyses are carried out to show the effects of parameters on the immunity-activated reproduction number $\mathscr{R}_{1}$ and the viral load.

Citation: Jian Ren, Rui Xu, Liangchen Li. Global stability of an HIV infection model with saturated CTL immune response and intracellular delay[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 57-68. doi: 10.3934/mbe.2021003

### Related Papers:

• In this paper, we consider an HIV infection model with saturated infection rate, intracellular delay and saturated cytotoxic T lymphocyte (CTL) immune response. By calculation, we obtain immunity-inactivated reproduction number $\mathscr{R}_0$ and immunity-activated reproduction number $\mathscr{R}_1$. By analyzing the distribution of roots of the corresponding characteristic equations, we study the local stability of an infection-free equilibrium, an immunity-inactivated equilibrium and an immunity-activated equilibrium of the model. By constructing suitable Lyapunov functionals and using LaSalle's invariance principle, we show that if $\mathscr{R}_0 < 1$, the infection-free equilibrium is globally asymptotically stable; If $\mathscr{R}_1 < 1 < \mathscr{R}_0$, the immunity-inactivated equilibrium is globally asymptotically stable; If $\mathscr{R}_1>1$, the immunity-activated equilibrium is globally asymptotically stable. Sensitivity analyses are carried out to show the effects of parameters on the immunity-activated reproduction number $\mathscr{R}_{1}$ and the viral load.

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