Publication: Modelos para el control de epidemias infecciosas: el impacto de la vacunación
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2021-02-25
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En este trabajo se realiza una revisión del modelo compartimental que contempla cuarentenas, hospitalizaciones y vacunación imperfecta propuesto por Safi, M. A. et al (2011) y se ratifican las conclusiones de este artículo. A este n, se establece un marco teórico que aborda conceptos claves de teoría de estabilidad, variedades centrales y bifurcación subcrítica. El modelo objeto de estudio presenta la coexistencia de un equilibrio libre de infección y un equilibrio endémico por debajo del umbral R0 = 1, poniendo en peligro la erradicación. Se proporcionan dos cuantificadores para la evaluación de la vacunación, buscando evitar el efecto pernicioso de una vacuna poco eficaz en la dinámica del modelo. Finalmente, se propone y se realiza un breve análisis del modelo modificado para una población antivacunas constante.
The compartmental model that contemplates quarantines, hospitalizations and imperfect vaccination proposed by Safi, M. A. et al (2011) is reviewed and the authors conclusions get ratiffed. Towards this, a proper theoretical framework that addresses key concepts of stability theory, central manifolds, and backward bifurcation is stablished. The model studied presents backward bifurcation, showing the coexistence of an disease free equilibrium and an endemic equilibrium below the threshold R0 = 1. Two quantifiers are provided for the vaccine assesment in order to avoid the harmful effect of a poorly effective vaccine on the dynamics of the model. Finally, I propose and carry out a brief analysis of a modiffication of the model with a constant anti-vaccine population.
The compartmental model that contemplates quarantines, hospitalizations and imperfect vaccination proposed by Safi, M. A. et al (2011) is reviewed and the authors conclusions get ratiffed. Towards this, a proper theoretical framework that addresses key concepts of stability theory, central manifolds, and backward bifurcation is stablished. The model studied presents backward bifurcation, showing the coexistence of an disease free equilibrium and an endemic equilibrium below the threshold R0 = 1. Two quantifiers are provided for the vaccine assesment in order to avoid the harmful effect of a poorly effective vaccine on the dynamics of the model. Finally, I propose and carry out a brief analysis of a modiffication of the model with a constant anti-vaccine population.
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