Geodesic
The Deterministic Evolution Of Illicit Drug Consumption Within a Given Population
Yusra Bibi Ruhomally1 ; Nabeelah Banon Jahmeerbaccus2 ; Muhammad Zaid Dauhoo1
1Department of Mathematics, Faculty of Science, University of Mauritius, Reduit, Mauritius
2Medical and Health Officer, Flacq Hospital, Mauritius
ESAIM. Proceedings, Tome 62 (2018), pp. 139-157
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We study the NERA model that describes the dynamic evolution of illicit drug usage in a population. The model consists of nonusers (N) and three categories of drug users: the experimental (E) category, the recreational (R) category and the addict (A) category. Two epidemic threshold term known as the reproduction numbers, R0 and μ are defined and derived. Sensitivity analysis of R0 on the parameters are performed in order to determine their relative importance to illicit drug prevalence. The local and global stability of the equilibrium states are also analysed. We also prove that a transcritical bifurcation occurs at R0 = 1. It is shown that an effective campaign of prevention can help to fight against the prevalence of illicit drug consumption. We demonstrate persistence when R0 > 1 and conditions for the extinction of drug consumption are also established. Numerical simulations are performed to verify our model. Our results show that the NERA model can assist policy makers in targeting prevention for maximum effectiveness and can be used to adopt evidence-based policies to better monitor and quantify drug use trends.
DOI : 10.1051/proc/201862139

Yusra Bibi Ruhomally  1   ; Nabeelah Banon Jahmeerbaccus  2   ; Muhammad Zaid Dauhoo  1

1 Department of Mathematics, Faculty of Science, University of Mauritius, Reduit, Mauritius
2 Medical and Health Officer, Flacq Hospital, Mauritius 
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     author = {Yusra Bibi Ruhomally and Nabeelah Banon Jahmeerbaccus and Muhammad Zaid Dauhoo},
     title = {The {Deterministic} {Evolution} {Of} {Illicit} {Drug} {Consumption} {Within} a {Given} {Population}},
     journal = {ESAIM. Proceedings},
     pages = {139--157},
     year = {2018},
     volume = {62},
     doi = {10.1051/proc/201862139},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201862139/}
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Yusra Bibi Ruhomally; Nabeelah Banon Jahmeerbaccus; Muhammad Zaid Dauhoo. The Deterministic Evolution Of Illicit Drug Consumption Within a Given Population. ESAIM. Proceedings, Tome 62 (2018), pp. 139-157. doi: 10.1051/proc/201862139

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