W. Liu [Dynamics of epidemiological models. Recurrent outbreaks in autonomous systems. Ph.D. Thesis, Cornell Univ./Ithaca (1987)] points out that the dynamical behavior of epidemics is usually very complicated and many infectious diseases exhibit recurrent outbreaks in large populations. In this respect Liu introduced and examined a quite general SEIRS epidemiological model. The SEIRS model involves a new class of populations, i.e., the exposed but not yet infectious class (E) in addition to susceptible (S), infectious (I) and recovered (R) classes. We will concentrate on an SIRS epidemiological model examined in detail by W. Liu et al. [J. Math. Biol. 23, 187-204 (1986; Zbl 0582.92023)]. The SIRS model can be regarded as the limiting case of the SEIRS model when the average latent periods tend to zero. We make a bifurcation analysis of this SIRS epidemiological model depending on all parameters. In particular we are interested in codimension-2 bifurcations.