El propósito del presente trabajo es presentar el concepto de matriz de transformación de bases B-spline (abreviado como matriz BSBT) y su aplicación en el manejo d las curvas B-spline. La matriz BSBT permite que una base B-spline pueda ser representada por otra, se presentará las condiciones de existencia y unicidad de esta matriz. Mostrando una relación recursiva de las matrices BSBT, para luego desarrollar un algoritmo que calcule dicha matriz, que sea eficiente y simple de implementar. Finalmente se verá su aplicación en dos problemas que se presentan en las curvas B-splines: la inserción de nodos y la elevación de grado, ya sea por separado o si multáneamente.

In the present work, the existence of Uniformly Bound Solutions of a SI Mathematical Model with vital dynamics, with logistic growth for the Susceptibles, developed by Delay Differential Equations is constructed, and the behavior of the solutions will be studied (qualitative analysis) for the Infection-Free Point where the necessary conditions for its asymptotic stability will be determined; and furthermore, that the Uniformly Bounded Solution of the Model tends to the steady state of the Infection-Free Point. In addition, it will be simulated computationally (approximate solutions) with initial populations and epidemiological rates of the model. The simulation will complement the qualitative analysis (behavior of solutions) to conclude trends of behaviors of the transmission of the disease overtime.

In the present work, the existence of Uniformly Bound Solutions of a SI Mathematical Model with vital dynamics, with logistic growth for the Susceptibles, developed by Delay Differential Equations is constructed, and the behavior of the solutions will be studied (qualitative analysis) for the Infection-Free Point where the necessary conditions for its asymptotic stability will be determined; and furthermore, that the Uniformly Bounded Solution of the Model tends to the steady state of the Infection-Free Point. In addition, it will be simulated computationally (approximate solutions) with initial populations and epidemiological rates of the model. The simulation will complement the qualitative analysis (behavior of solutions) to conclude trends of behaviors of the transmission of the disease overtime.