This paper proposes a stochastic model with discrete delay coefficients for modeling population dynamics. This model is a memory-modulated version of the well known CIR process. Existence and uniqueness of the global solution and non-negativity of the solution are discussed. Significantly, results concerning persistence of the population and other longterm qualitative behaviors of these non-Markov processes are obtained using hitting times. Under particular parameter values, the model exhibits

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... eflection at the zero boundary and so models populations that persist due to the influence of past population.