Multiparametric bifurcations of an epidemiological model with strong Allee effect.

摘要: In this paper we completely study bifurcations of an epidemic model with five parameters introduced by Hilker et al. (Am Nat 173:72–88, 2009), which describes the joint interplay a strong Allee effect and infectious diseases in single population. Existence multiple positive equilibria all kinds bifurcation are examined as well related dynamical behavior. It is shown that undergoes series such saddle-node bifurcation, pitchfork Bogdanov–Takens degenerate Hopf codimension two elliptic type three. Respective surfaces five-dimensional parameter spaces behavior obtained. These theoretical conclusions confirm their numerical simulations conjectures al., reveal some new phenomena not observed 2009). The rich complicated dynamics exhibit very sensitive to perturbations, has important implications for disease control endangered species.