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Oleg Jakovlevich Kravets, Igor Viktorovich Atlasov, Vladimir Dmitriyevich Sekerin, Anna Evgenievna Gorokhova, Sergey Kurbanovich Gasanbekov


When examining a large group of people and provided that very few people get sick (the probability of a disease), there is a technique to diagnose the disease that allows reducing the use of drugs necessary for diagnosing the disease. A set of all people (total - n) is divided arbitrarily into groups of k people (k>1). Then the blood of these k people is mixed and a part is drawn for a single analysis. If it is possible to find k so that practically in all of these groups there will be no patients with a disease, the quantity of the chemicals used for diagnosing can be reduced approximately k times. Section I (introduction) describes this problem. In section II the proposed methodology is discussed. The first improved model include the problem of finding the maximum natural value of k arises, so that almost all of these groups of k people include no sick people. The second improved model shows that it is possible to further reduce the use of resources due to the fact that if a virus is found in the fluid collected from a group of k people and the first k-1 people are healthy, then the last person should not be checked, since it is definitely infected. The idea of the third improved model is based on the fact that the group can also be divided into smaller groups and, under certain circumstances, the blood will be drawn not from each individual, but in small groups. The fourth improved model consider the generalized technique. The section III (conclusion) confirms that the scope of the proposed methods is wider than that of the existing ones, using a numerical example.


extremum; mathematical expectation; random function

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