Optimal control of alcoholism spreading through awareness over multiplex network  

作　　者：Padmavathi Ramamoorthi Senthil Kumar Muthukrishnan 

机构地区：[1]Department of Science and Humanities Info Institute of Engineering,Coimbatore,India [2]Department of Applied Mathematics and Computational Sciences PSG College of Technology,Coimbatore,India

出　　处：《International Journal of Biomathematics》2021年第6期33-58,共26页生物数学学报（英文版）

摘　　要：This paper proposes the SISRS epidemic model to represent alcohol addiction among people.The spreading of alcohol addiction is controlled by creating awareness among the people and also by treating them to overcome it.Multiplex network is used to study the dynamics of addiction.Alcoholism spreads over the physical contact layer and follows the SISRS process whereas human awareness spreads over the virtual contact layer and follows the UAU process.Based on the Microscopic Markov Chain Approach competing dynamics of spreading of alcohol addiction and human awareness diffusion are studied.Necessary conditions for the existence of an alcohol-free population are found.An optimal control problem using a suitable cost index is formulated to reduce the alcohol addicts and the optimal control strategy using Pontryagin’s Minimum Principle is determined.Numerical results are developed to find the effect of various parameters and to analyze the effects of different control strategies.The results obtained from this model are closer to the data collected in the National Survey of Drug Use and Health(NSDUH)from 2002 to 2018.

关 键 词：Alcohol spreading information diffusion Microscopic Markov Chain Approach optimal control 

分 类 号：O17[理学—数学]