Global stability for a HIV/AIDS model

TORRES, SILVA Cristiana J.;

doi:10.1501/commua1_0000000833

Cited by 11 publications

(2 citation statements)

References 23 publications

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“…Here we propose a Caputo fractional order SICA epidemiological model with constant recruitment rate, mass action incidence and variable population size, for HIV/AIDS transmission. The model is based on an integer-order HIV/AIDS model without memory effects firstly proposed in [17] and later modified in [18,19]. The model for α = 1 describes well the clinical reality given by the data of HIV/AIDS infection in Cape Verde from 1987 to 2014 [18].…”

Section: Introductionmentioning

confidence: 99%

Stability of a fractional HIV/AIDS model

Silva

Torres

2019

Mathematics and Computers in Simulation

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Section: Introductionmentioning

confidence: 99%

Stability of a fractional HIV/AIDS model

Silva

Torres

2019

Mathematics and Computers in Simulation

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“…The immune system is represented by the cytotoxic T lymphocytes (CTLs) and antibodies respond to their message by attacking and killing the infected cells and HIV virus. In the last decades, many mathematical models have been developed to better describe and understand the dynamics of the HIV disease, e.g., [8,14,17,25,26]. An HIV model with adaptive immune response, two saturated rates, and therapy, is studied in [2], showing that the goal of immunity response is controlling the load of HIV viruses.…”

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confidence: 99%

Optimal control of an HIV model with a trilinear antibody growth function

Allali¹,

Harroudi²,

Torres³

2022

DCDS-S

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<p style='text-indent:20px;'>We propose and study a new mathematical model of the human immunodeficiency virus (HIV). The main novelty is to consider that the antibody growth depends not only on the virus and on the antibodies concentration but also on the uninfected cells concentration. The model consists of five nonlinear differential equations describing the evolution of the uninfected cells, the infected ones, the free viruses, and the adaptive immunity. The adaptive immune response is represented by the cytotoxic T-lymphocytes (CTL) cells and the antibodies with the growth function supposed to be trilinear. The model includes two kinds of treatments. The objective of the first one is to reduce the number of infected cells, while the aim of the second is to block free viruses. Firstly, the positivity and the boundedness of solutions are established. After that, the local stability of the disease free steady state and the infection steady states are characterized. Next, an optimal control problem is posed and investigated. Finally, numerical simulations are performed in order to show the behavior of solutions and the effectiveness of the two incorporated treatments via an efficient optimal control strategy.</p>

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A qualitative analysis of aMycoplasma genitaliumepidemiological model

Almeida

Monteiro

Venturino

et al. 2021

Comp and Math Methods

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The objective of the article is to present a qualitative analysis of a mathematical model for the spread of a sexually transmitted infection caused by Mycoplasma genitalium. Recent investigations revealed that this pathogen is becoming resistant to the use of macrolides and can turn into a superbug in the next few years. We present an epidemiological model to describe the spread of the disease. The equilibrium points are computed, and their local and global stability are studied. In order to make the mathematical problem more realistic, we propose two different optimal control problems that establish a balance between the number of infected individuals and the use of macrolides. Several numerical illustrations regarding the solutions of the proposed problems will be provided.

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Global stability for a HIV/AIDS model

Cited by 11 publications

References 23 publications

Stability of a fractional HIV/AIDS model

Stability of a fractional HIV/AIDS model

Optimal control of an HIV model with a trilinear antibody growth function

A qualitative analysis of aMycoplasma genitaliumepidemiological model

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