Time-varying pharmacodynamics in a simple non-integer HIV infection model

Pinto, Carla M. A.; Carvalho, Ana R.M.; Tavares, João Nuno

doi:10.1016/j.mbs.2018.11.001

Cited by 14 publications

(3 citation statements)

References 28 publications

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“…Since the first AIDS case was discovered in 1981 [1], HIV has spread worldwide and over 35 million people have died from AIDS-related illness. At the end of 2016, approximately 36.7 million people were living with HIV, and approximately 1.8 million new infections were occurring globally each year [2]. According to UNAIDS data reported in June 2016 [3], around 18.2 million people living with HIV were receiving antiretroviral therapy (ART).…”

Section: Introductionmentioning

confidence: 99%

“…This number has more than doubled since 2010, while AIDS-related deaths in these regions have decreased by 38% since 2010. Some official reports indicate that between 2000 and 2016 in Africa, HIV-related deaths fell by one-third and the ART helped in saving 13.1 million lives [2]. Although the antiretroviral therapy cannot completely eliminate the virus, it can reduce the level sufficiently to prevent transmission from an HIV+ person to an uninfected person.…”

Section: Introductionmentioning

confidence: 99%

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A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

2019

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In recent years, many new definitions of fractional derivatives have been proposed and used to develop mathematical models for a wide variety of real-world systems containing memory, history, or nonlocal effects. The main purpose of the present paper is to develop and analyze a Caputo-Fabrizio fractional derivative model for the HIV/AIDS epidemic which includes an antiretroviral treatment compartment. The existence and uniqueness of the system of solutions of the model are established using a fixed-point theorem and an iterative method. The model is shown to have a disease-free and an endemic equilibrium point. Conditions are derived for the existence of the endemic equilibrium point and for the local asymptotic stability of the disease-free equilibrium point. The results confirm that the disease-free equilibrium point becomes increasingly stable as the fractional order is reduced. Numerical simulations are carried out using a three-step Adams-Bashforth predictor method for a range of fractional orders to illustrate the effects of varying the fractional order and to support the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

2019

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“…In fact, drugs are often administered for patients periodically. As we known, drug concentration will reach a peak value within a very short time when a dose is administrated, and the concentration down to a lower value as time goes and then reaches a peak value again when another dose is administrated [14][15][16].…”

Section: Introductionmentioning

confidence: 95%

Threshold Dynamics for a Time-Periodic Viral Infection Model with Cell-to-Cell Transmission and Drug Treatments

Huang

2022

Mathematical Problems in Engineering

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In this study, a time-periodic viral infection model incorporating cell-to-cell infection and antiretroviral therapy has been investigated. The basic reproduction number ℛ 0 has been defined as a threshold parameter which governs whether or not the disease dies out. Theoretical results indicate that the disease goes to extinction if ℛ 0 < 1 and otherwise the disease will uniformly persist. The global stabilities of the equilibria for the corresponding autonomous model have been investigated by constructing suitable Lyapunov functions. Moreover, numerical simulations have been carried out to validate the obtained results. The results show that cell-to-cell infection mode may be a barrier to curing the viral infection and increasing the efficacy of protease inhibitors for blocking cell-to-cell infection which will benefit to weaken the severity of the viral infection.

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Role of the Immune System in AIDS-defining Malignancies

Carvalho

Pinto

2021

Springer Proceedings in Mathematics &Amp; Statistics

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Time-varying pharmacodynamics in a simple non-integer HIV infection model

Cited by 14 publications

References 28 publications

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

Threshold Dynamics for a Time-Periodic Viral Infection Model with Cell-to-Cell Transmission and Drug Treatments

Role of the Immune System in AIDS-defining Malignancies

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