Complex dynamics in a discrete SIS epidemic model with Ricker-type recruitment and disease-induced death

Abstract

In this paper, we investigate the complex dynamics in a discrete SIS epidemic model with Ricker-type recruitment and disease-induced death. It is shown that the model has a unique disease-free equilibrium if the basic reproduction number $${\mathcal {R}}_{0}\le 1$$ and a unique endemic equilibrium if $${\mathcal {R}}_{0}> 1$$ . Sufficient conditions for the locally asymptotic stability of the equilibria are obtained. A detailed bifurcation analysis at the endemic equilibrium reveals that the model undergoes a sequence of bifurcations, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation, as the parameters vary. Various numerical simulations, including bifurcation diagrams, phase portraits, maximum Lyapunov exponents and feasible sets, are carried out to present complex periodic windows, period-28 points, multiple chaotic bands, fractal basin boundaries, chaotic attractors and the coexistence of period points and three invariant tori, which not only illustrate the theoretical results but also demonstrate more complex dynamical behaviors of the model.