Solución Uniformemente Acotada y Estabilidad Asintótica del Punto Libre de Infección de un Modelo Matemático SI con Dinámica Vital (crecimiento logístico) mediante las Ecuaciones Diferenciales con Retardo

Abstract

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 pidemiological 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 over time.

Keywords

• Epidemiología Matemática
• Ecuaciones Diferenciales Ordinarias
• Ecuaciones Diferenciales con Retardo
• Puntos Estacionarios
• Estabilidad Local
• Estabilidad Absoluta