DOI:
https://doi.org/10.14483/23448350.23342Published:
02/11/2026Issue:
Vol. 52 No. 3 (2025): August-December 2025Section:
Research ArticlesEstabilidad global en un modelo para la dinámica del VIH/SIDA, considerando inmigración, diagnóstico y tratamiento antirretroviral
Global Stability in a Model for HIV/AIDS Dynamics, Considering Immigration, Diagnosis, and Antiretroviral Treatment
Keywords:
global stability, antiretroviral therapy, inmigration, HIV/AIDS (en).Keywords:
estabilidad global, terapia antirretroviral, inmigración, VIH/SIDA (es).Downloads
Abstract (es)
En este artículo se presenta un modelo matemático para la dinámica del VIH/SIDA que incluye inmigración y trasmisión vertical, diagnóstico y terapia antirretroviral (TAR). El modelo considera cinco grupos de población: individuos susceptibles, individuos infectados no diagnosticados, individuos diagnosticados con SIDA, individuos diagnosticados con infección no detectable e individuos diagnosticados con infección detectable. Posteriormente, se analiza el modelo sin inmigración y trasmisión vertical. Para ambos modelos, se determinan los puntos de equilibrio y la estabilidad global. Las simulaciones numéricas respaldan los resultados teóricos, ilustrando el impacto del TAR en el control de la propagación del VIH. Los hallazgos refuerzan la importancia del diagnóstico temprano y la adherencia al TAR, así como disminuir las tasas de migración y transmisión vertical para reducir la transmisión y mejorar la expectativa de vida.
Abstract (en)
This work presents a mathematical model for the dynamics of HIV/AIDS with immigration and vertical transmission, diagnosis, and antiretroviral therapy (ART). The model considers five population groups: susceptible individuals, undiagnosed infected individuals, individuals diagnosed with AIDS, diagnosed individuals with an undetectable infection, and diagnosed individuals with a detectable infection. Afterwards, the model without immigration and vertical transmission is analyzed. For both models, the equilibrium points and global stability are determined. Numerical simulations support the theoretical results, illustrating the impact of ART in controlling the spread of HIV. The findings reinforce the importance of early diagnosis and adherence to ART, as well as the importance of decreasing migration and vertical transmission rates in order to reduce transmission and improve life expectancy.
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Copyright (c) 2026 José Armando Ortega, Miller Orlando Cerón, Eduardo Ibarguen Mondragon
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