Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a Case Study in San Juan de Pasto, Colombia

Morillo, Cristian Camilo Espitia; Botina, Miguel A; Solarte, Marco A; Hernández, Iván; Riascos, Ricardo A; Meyer, John-Jules

doi:10.1089/cmb.2021.0323

Cited by 9 publications

(5 citation statements)

References 26 publications

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“…The epidemiological model under consideration was studied in [8], it contains three population groups: the first men with homosexual preference in men, the second one men with heterosexual preference and the third one for women who may be homosexuals or heterosexuals, but engage in sexual relations with homosexual or heterosexual men. We supposed that eventually homosexual men had sexual contact with women, and that heterosexual men had sexual relation with homosexual men.…”

Section: Methodsmentioning

confidence: 99%

“…This means that susceptible homosexual men selects their partner randomly from the infected homosexual population, while women or men selects her/his partner randomly from the infected heterosexual or infected homosexual population. Adapted of [8].. The force of infection or disease incidence function measures the susceptible person's risk to becoming infected.…”

Section: Parameters In the Modelmentioning

confidence: 99%

“…Proof. LAS will be demonstrate with the eigenvalues of jacobian matrix related to the system (1) to (8) evaluated in E 0 , it is…”

Section: Local Stability Of Disease Free Equilibriummentioning

confidence: 99%

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HIV/AIDS Mathematical Model of Triangle Transmission

Morillo¹,

Meyer²

2022

Preprint

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In this paper mathematical analysis of the HIV/AIDS deterministic model exposed in [Espitia, C. et. al. Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a Case Study in San Juan de Pasto, Colombia, Journal of Computational Biology 29 (2022) 483–493] is made. The objective is to gain insight into the qualitative dynamics of the model determining the conditions for the persistence or effective control of the disease in the community through the study of basic properties such as positiveness and boundedness, calculus of basic reproduction number, stationary points such as disease free equilibrium (DFE), boundary equilibrium (BE) and endemic equilibrium (EE) are calculated, local stability (LAS) of disease free equilibrium. It research allow to conclude that the best way to reduce contagion and consequently to reach a DFE is thought to be the reduction of homosexual partners rate as they are the most affected population by the virus, and are therefore the most likely to become infected and to spread the infection. Increasing the departure rate of infected individuals, leads to a decrease in untreated infected heterosexual men and untreated infected women.

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Section: Methodsmentioning

confidence: 99%

Section: Parameters In the Modelmentioning

confidence: 99%

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HIV/AIDS Mathematical Model of Triangle Transmission

Morillo¹,

Meyer²

2022

Preprint

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“…Ensuring the halt of the HIV/AIDS epidemic is of utmost importance, and this objective can be attained through the implementation of efficient and effective strategies, prominently including HIV/AIDS treatment. One such crucial treatment available to infected individuals is antiretroviral therapy (ART) [6,7]. By preventing transmission between sexual partners, these therapeutic interventions play a pivotal role.…”

Section: Introductionmentioning

confidence: 99%

A mathematical and sensitivity analysis of an HIV/AIDS infection model

Ahmed,

Tariboon,

Muhammad

et al. 2024

International Journal of Mathematics and Computer in Engineering

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Over the past decade, Human Immunodeficiency Virus infection and Acquired Immunodeficiency Syndrome (HIV/AIDS) have become deadly infectious diseases, particularly in developing countries. This challenge has led to the development of some important HIV/AIDS treatment strategies, such as antiretroviral therapy (ART), among many others. This study presents a mathematical model to investigate the dynamics of HIV/AIDS transmission. Employing mathematical analysis, non-negativity, boundedness, the basic reproduction number ℛ 0, and the stability of both the disease-free and endemic equilibrium of the proposed model were derived. Normalized forward sensitivity techniques are used to determine the significance and importance of sensitive parameters associated with ℛ 0. To gain insights into the dynamical behavior of each compartment, an effective numerical scheme was utilized, and the results obtained suggest that there is a need, even if individuals are infected with the virus, to use non-pharmaceutical interventions as control strategies.

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“…The authors in [ 26 ] constructed a compartmental model by extending the concept of awareness and unawareness used in [ 25 ] for HIV/AIDS with optimal control analysis under the reported data of Ethiopia. In [ 27 ], the sexual and ART have been considered. They considered the real data for the period 1989–2019 and obtained the results.…”

Section: Introductionmentioning

confidence: 99%

Analysis and simulation study of the HIV/AIDS model using the real cases

Meetei,

DarAssi,

Altaf Khan

et al. 2024

PLoS ONE

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We construct a model to investigate HIV/AIDS dynamics in real cases and study its mathematical analysis. The study examines the qualitative outcomes and confirms the local and global asymptotic stability of both the endemic equilibrium and the disease-free equilibrium. The model’s criteria for exhibiting both local and global asymptotically stable behavior are examined. We compute the endemic equilibria and obtain the existence of a unique positive endemic equilibrium. The data is fitted to the model using the idea of nonlinear least-squares fitting. Accurate parameter values are achieved by fitting the data to the model using a 95% confidence interval. The basic reproduction number is computed using parameters that have been fitted or estimated. Sensitivity analysis is performed to discover the influential parameters that impact the reproduction number and the eradication of the disease. The results show that implementing preventive measures can reduce HIV/AIDS cases.

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Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a Case Study in San Juan de Pasto, Colombia

Cited by 9 publications

References 26 publications

HIV/AIDS Mathematical Model of Triangle Transmission

HIV/AIDS Mathematical Model of Triangle Transmission

A mathematical and sensitivity analysis of an HIV/AIDS infection model

Analysis and simulation study of the HIV/AIDS model using the real cases

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