Título: Local and Global Stability of Host-Vector Disease Models
Autores: Cruz Vargas de León, Jorge Armando Castro Hernández


In this work we deal with global stability properties of two host - vector disease models using the Poicare-Bendixson Theorem and Second Method of Lyapunov. We construct a Lyapunov function for each Vector- Host model. We proved that the local and global stability are completely determined by the threshold parameter, R_0. If R_0 minor o equal 1, the disease-free equilibrium point is globally asymptotically stable. If R_0 > 1, a unique endemic equilibrium point exists and is globally asymptotically stable in the interior of the feasible region.

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