In the present paper we make a bifurcation analysis of an SIRS epidemiological model depending on all parameters. In particular we are interested in codimension-2 bifurcations.

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In this paper we characterize partially the global dynamic of a predator prey model with non constant mortality rate. Concretely, we give necessary and sufficient conditions in order the system be dissipative and permanent. We study the global stability of the nontrivial equilibrium, when it is unique. We show that it is possible the existence of a unique periodic solution which arises from a supercritical Hopf bifurcation and end up through a subcritical Hopf bifurcation; suggesting that the model exhibits new dynamical features which are not present in the classical model; i.e., in the model with constant mortality rate.