Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells

Zhang, Tongqian; Wang, Junling; Song, Yi; Jiang, Zhichao

doi:10.1155/2020/2313102

Cited by 3 publications

(1 citation statement)

References 52 publications

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“…The global stability of the equilibria is shown below by constructing two Lyapunov functionals under fractional derivatives of state variables. The methods and techniques given in the work of Zhang et al [32] are followed to prove the following results.…”

Section: Stability Of the Equilibriamentioning

confidence: 99%

Fractional‐order models of hepatitis B virus infection with recycling effects of capsids

Sutradhar,

Dalal

2023

Math Methods in App Sciences

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Hepatitis B virus (HBV) infection is a major public health concern throughout the world. It can be treated effectively through proper medication and vaccination, although it is very difficult to cure, especially in people who have had the chronic infection. So, it is necessary to pay proper attention for its eradication. In this study, two nonlinear fractional‐order HBV infection models with recycling effects of capsids are presented via the Caputo derivative. Each model contains four compartments, namely, susceptible hepatocytes, infected hepatocytes, HBV capsids, and viruses. In the first model, the order of fractional derivatives is equal for each compartment, whereas, in the second model, the order is incommensurate. The existence and uniqueness of solutions for both models are discussed separately. The parameters are estimated in order to validate the proposed model with experimental data obtained from a chimpanzee. Stability analyses are carried out for both models theoretically. The models are solved numerically using the predictor–corrector Adams–Bashforthm–Moulton method (for commensurate order) and implicit product integration of trapezoidal type method (for incommensurate order) with various choices of fractional orders and initial conditions. All the results are presented graphically. Interestingly, the results reveal the importance of fractional‐order derivatives in capturing the dynamics of HBV transmission in the host. It is also noticed that with the decrease in the order of fractional derivative, the peak level of infection decreases, but the disease takes a long time to be cured.

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Section: Stability Of the Equilibriamentioning

confidence: 99%

Fractional‐order models of hepatitis B virus infection with recycling effects of capsids

Sutradhar,

Dalal

2023

Math Methods in App Sciences

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Uniform Persistence and Global Attractivity in a Delayed Virus Dynamic Model with Apoptosis and Both Virus-to-Cell and Cell-to-Cell Infections

Guo

2022

Mathematics

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In this paper, we study the global dynamics of a delayed virus dynamics model with apoptosis and both virus-to-cell and cell-to-cell infections. When the basic reproduction number R0>1, we obtain the uniform persistence of the model, and give some explicit expressions of the ultimate upper and lower bounds of any positive solution of the model. In addition, by constructing the appropriate Lyapunov functionals, we obtain some sufficient conditions for the global attractivity of the disease-free equilibrium and the chronic infection equilibrium of the model. Our results extend existing related works.

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A delayed dynamical model for COVID-19 therapy with defective interfering particles and artificial antibodies

Zhao

Xing

2022

DCDS-B

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<p style='text-indent:20px;'>In this paper, we use delay differential equations to propose a mathematical model for COVID-19 therapy with both defective interfering particles and artificial antibodies. For this model, the basic reproduction number <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{R}_0 $\end{document}</tex-math></inline-formula> is given and its threshold properties are discussed. When <inline-formula><tex-math id="M2">\begin{document}$ \mathcal{R}_0<1 $\end{document}</tex-math></inline-formula>, the disease-free equilibrium <inline-formula><tex-math id="M3">\begin{document}$ E_0 $\end{document}</tex-math></inline-formula> is globally asymptotically stable. When <inline-formula><tex-math id="M4">\begin{document}$ \mathcal{R}_0>1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ E_0 $\end{document}</tex-math></inline-formula> becomes unstable and the infectious equilibrium without defective interfering particles <inline-formula><tex-math id="M6">\begin{document}$ E_1 $\end{document}</tex-math></inline-formula> comes into existence. There exists a positive constant <inline-formula><tex-math id="M7">\begin{document}$ R_1 $\end{document}</tex-math></inline-formula> such that <inline-formula><tex-math id="M8">\begin{document}$ E_1 $\end{document}</tex-math></inline-formula> is globally asymptotically stable when <inline-formula><tex-math id="M9">\begin{document}$ R_1<1<\mathcal{R}_0 $\end{document}</tex-math></inline-formula>. Further, when <inline-formula><tex-math id="M10">\begin{document}$ R_1>1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M11">\begin{document}$ E_1 $\end{document}</tex-math></inline-formula> loses its stability and infectious equilibrium with defective interfering particles <inline-formula><tex-math id="M12">\begin{document}$ E_2 $\end{document}</tex-math></inline-formula> occurs. There exists a constant <inline-formula><tex-math id="M13">\begin{document}$ R_2 $\end{document}</tex-math></inline-formula> such that <inline-formula><tex-math id="M14">\begin{document}$ E_2 $\end{document}</tex-math></inline-formula> is asymptotically stable without time delay if <inline-formula><tex-math id="M15">\begin{document}$ 1<R_1<\mathcal{R}_0<R_2 $\end{document}</tex-math></inline-formula> and it loses its stability via Hopf bifurcation as the time delay increases. Numerical simulation is also presented to demonstrate the applicability of the theoretical predictions.</p>

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Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells

Cited by 3 publications

References 52 publications

Fractional‐order models of hepatitis B virus infection with recycling effects of capsids

Fractional‐order models of hepatitis B virus infection with recycling effects of capsids

Uniform Persistence and Global Attractivity in a Delayed Virus Dynamic Model with Apoptosis and Both Virus-to-Cell and Cell-to-Cell Infections

A delayed dynamical model for COVID-19 therapy with defective interfering particles and artificial antibodies

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