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Abstract: This paper examines how optimal prevention and control policies depend on the economic and biological characteristics of a randomly introduced biological invasion where the objective is to minimize the expected social costs from prevention, control, and invasion damages. The results characterize how optimal prevention and control policies vary with the initial invasion size, the invasion growth rate, and the probability distribution of introductions. The paper also examines the conditions under which the optimal policy relies solely on either prevention or control, the conditions under which it is optimal to completely prevent new introductions, and the conditions under which eradication of established invasions is optima