Palabras clave
stability
optimal control
Pontryagin maximum principle
HIV
antirretroviral therapy
sistemas dinámicos
estabilidad
control óptimo
principio del máximo de Pontryagin
VIH
terapia antirretroviral
Cómo citar
Resumen
Se propone un modelo en ecuaciones diferenciales ordinarias para describir la dinámica de infección por VIH en una población de células T CD4 susceptibles a la infección y considerando una tasa de infección no lineal densodependiente. Se analiza la estabilidad del modelo con base en el número básico de reproducción, lo que permite determinar resultados de estabilidad y un umbral de control mediante la reducción de la tasa máxima de infección. Luego se formula un problema de control óptimo para establecer funciones óptimas de tratamiento mediante inhibidores de transcriptasa inversa e inhibidores de proteasa, que minimicen la carga viral y los costos directos y/o indirectos de la administración del tratamiento. Se estudian los casos en que la efectividad del tratamiento es nula y plena, y para el caso de efectividad imperfecta del tratamiento se acude al Principio del Máximo de Pontryagin. Se presentan simulaciones numéricas del modelo sin tratamiento y de los diferentes escenarios con tratamiento.
Citas
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