{"title":"哥伦比亚大学生酗酒蔓延的数学模型","authors":"E. Pérez","doi":"10.17230/ingciencia.16.32.9","DOIUrl":null,"url":null,"abstract":"In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.","PeriodicalId":30405,"journal":{"name":"Ingenieria y Ciencia","volume":"16 1","pages":"195-223"},"PeriodicalIF":0.0000,"publicationDate":"2020-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students\",\"authors\":\"E. Pérez\",\"doi\":\"10.17230/ingciencia.16.32.9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.\",\"PeriodicalId\":30405,\"journal\":{\"name\":\"Ingenieria y Ciencia\",\"volume\":\"16 1\",\"pages\":\"195-223\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-11-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ingenieria y Ciencia\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17230/ingciencia.16.32.9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ingenieria y Ciencia","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17230/ingciencia.16.32.9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students
In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.
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