Different types of backward bifurcations on account of an improvement in treatment efficiency

• Autores: Osvaldo Osuna, Shaday Guerrero Flores, Geiser Villavicencio Pulido
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 36, Nº. 1, 2018 (Ejemplar dedicado a: Revista Integración, temas de matemáticas), págs. 21-35
• Idioma: inglés
• DOI: 10.18273/revint.v36n1-2018002
• Títulos paralelos:
  • Diferentes tipos de bifurcación hacia atrás a causa de una mejora en la eficiencia del tratamiento
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• Resumen
  • español

    Comprender por qué existen estados endémicos múltiples cuando R0 < 1 ha sido una de las principales motivaciones para analizar la existencia de una bifurcación hacia atrás en modelos epidemiológicos. La existencia de estados endémicos múltiples está asociada usualmente a ramas de puntos deequilibrio del sistema, las cuales pueden surgir ya sea desde el equilibrio libre de enfermedad si R0 = 1, o desde un equilibrio no trivial si R0 > 1. En este trabajo se analiza un modelo del tipo SIR con una tasa de tratamiento densodependiente. Se explica la naturaleza del punto de donde surge la bifurcación hacia atrás en función de la velocidad de la tasa de tratamiento per cápita. Se propondrán estrategias para el control o erradicación de la enfermedad en función de la eficiencia del tratamiento.

  • English

    Understanding why there are multiple equilibrium points when R0 < 1 has been one of the main motivations to analyze existence of a backward bifurcation in epidemiological models. Existence of multiple endemicstates is usually associated to branches of equilibrium points of the models, which could arise from either the disease-free equilibrium point if R0 = 1 or from an endemic equilibrium point if R0 > 1. In this work, an SIR model with a density-dependent treatment rate is analyzed. The nature of the point where backward bifurcation emerges is explained in function of the velocity of the per-capita treatment rate. Strategies for the control or eradication of the disease will be proposed in function of the efficiency of the treatment.

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