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Moreover, it is shown that there exists a critical value α 0 for the psychological effect α , a critical value k 0 for the infection rate k, and two critical values β 0 , β 1 ( β 1 less then β 0 ) for β that will determine whether the disease dies out or persists in the form of positive periodic coexistent oscillations or coexistent steady states under different initial populations. Numerical simulations are given to demonstrate the existence of one, two or three limit cycles.Random diffusive age-structured population models have been