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It is practically impossible to discuss the problem of bioterrorism (BT) and to develop effective programs of decreasing the losses and expenses suffered by the society from the BT acts without evaluation of the threat and prognosis of consequences based on research and empiric data. Stained international situation following the act of terrorism (attack on the USA) on September 11, 2001, makes the scenarios of the bacterial weapon use (the causative agents of plague, smallpox, anthrax, etc.) by international terrorists most probable. In this connection studies on the analysis and prognostication of the consequences of BT, including mathematical and computer modelling, are necessary. The authors present the results of initiative studies on the analysis and prognostication of the consequences of the hypothetical act of BT with the use of the smallpox causative agent in a city with the population of about 1,000,000 inhabitants. The analytical prognostic studies on the operative analysis and prognostication of the consequences of the BT act with the use of the smallpox causative agent has demonstrated that the mathematical (computer) model of the epidemic outbreak of smallpox is an effective instrument of calculation studies. Prognostic evaluations of the consequences of the act of BT under the conditions of different reaction of public health services (time of detection, interventions) have been obtained with the use of modelling. In addition, the computer model is necessary for training health specialists to react adequately to the acts of BT with the use of different kinds of bacteriological weapons.