Nonmonotone incidence and saturated treatment are incorporated into an SIRS model under constant and changing environments. The nonmonotone incidence rate describes the psychological or inhibitory effect: when the number of the infected individuals exceeds a certain level, the infection function decreases. The saturated treatment function describes the effect of infected individuals being delayed for treatment due to the limitation of medical resources. In a constant environment, the model undergoes a sequence of bifurcations including backward bifurcation, degenerate Bogdanov-Takens bifurcati...
