Modelling the role of drug barons on the prevalence of drug epidemics
Substance abuse is a global menace with immeasurable consequences to the health of users, the quality of life and the economy of countries affected. Although the prominently known routes of initiation into drug use are; by contact between potential users and individuals already using the drugs and s...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.843 |
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| author | John Boscoh H. Njagarah Farai Nyabadza |
| author_facet | John Boscoh H. Njagarah Farai Nyabadza |
| author_sort | John Boscoh H. Njagarah |
| collection | DOAJ |
| description | Substance abuse is a global menace with immeasurable consequences to the health of users, the quality of life and the economy of countries affected. Although the prominently known routes of initiation into drug use are; by contact between potential users and individuals already using the drugs and self initiation, the role played by a special class of individuals referred to as drug lords can not be ignored. We consider a simple but useful compartmental model of drug use that accounts for the contribution of contagion and drug lords to initiation into drug use and drug epidemics. We show that the model has a drug free equilibrium when the threshold parameter $R_{0}$ is less that unity and a drug persistent equilibrium when $R_{0}$ is greater than one. In our effort to ascertain the effect of policing in the control of drug epidemics, we include a term accounting for law enforcement. Our results indicate that increased law enforcement greatly reduces the prevalence of substance abuse. In addition, initiation resulting from presence of drugs in circulation can be as high as seven times higher that initiation due to contagion alone. |
| format | Article |
| id | doaj-art-5a9c74f761f64bbb88b64d5bf1ca8444 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5a9c74f761f64bbb88b64d5bf1ca84442025-01-24T02:26:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-03-0110384386010.3934/mbe.2013.10.843Modelling the role of drug barons on the prevalence of drug epidemicsJohn Boscoh H. Njagarah0Farai Nyabadza1Department of Mathematical Science, University of Stellenbosch, Private Bag X1, Matieland, Stellenbosch 7602Department of Mathematical Science, University of Stellenbosch, Private Bag X1, Matieland, Stellenbosch 7602Substance abuse is a global menace with immeasurable consequences to the health of users, the quality of life and the economy of countries affected. Although the prominently known routes of initiation into drug use are; by contact between potential users and individuals already using the drugs and self initiation, the role played by a special class of individuals referred to as drug lords can not be ignored. We consider a simple but useful compartmental model of drug use that accounts for the contribution of contagion and drug lords to initiation into drug use and drug epidemics. We show that the model has a drug free equilibrium when the threshold parameter $R_{0}$ is less that unity and a drug persistent equilibrium when $R_{0}$ is greater than one. In our effort to ascertain the effect of policing in the control of drug epidemics, we include a term accounting for law enforcement. Our results indicate that increased law enforcement greatly reduces the prevalence of substance abuse. In addition, initiation resulting from presence of drugs in circulation can be as high as seven times higher that initiation due to contagion alone.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.843reproduction numberdrug baronscontagionlaw enforcement. |
| spellingShingle | John Boscoh H. Njagarah Farai Nyabadza Modelling the role of drug barons on the prevalence of drug epidemics Mathematical Biosciences and Engineering reproduction number drug barons contagion law enforcement. |
| title | Modelling the role of drug barons on the prevalence of drug epidemics |
| title_full | Modelling the role of drug barons on the prevalence of drug epidemics |
| title_fullStr | Modelling the role of drug barons on the prevalence of drug epidemics |
| title_full_unstemmed | Modelling the role of drug barons on the prevalence of drug epidemics |
| title_short | Modelling the role of drug barons on the prevalence of drug epidemics |
| title_sort | modelling the role of drug barons on the prevalence of drug epidemics |
| topic | reproduction number drug barons contagion law enforcement. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.843 |
| work_keys_str_mv | AT johnboscohhnjagarah modellingtheroleofdrugbaronsontheprevalenceofdrugepidemics AT farainyabadza modellingtheroleofdrugbaronsontheprevalenceofdrugepidemics |