The Deterministic Evolution Of Illicit Drug Consumption Within a Given Population

Abstract

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 terms 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.

The NERA model incorporating cellular automata approach and the analysis of the resulting induced stochastic mean field

“…Recently, the deterministic NERA models of Dauhoo et al (2013) and Badurally Adam et al (2015) were revisited and were further analysed in Ruhomally et al (2018). In the latter work, the authors derived two reproduction numbers, R 0 and μ, which were used to analyse the stability of the system.…”

“…Sensitivity analysis was conducted on the parameters of R 0 and the calculated sensitivity indices were used to scrutinise the model. In the work of Dauhoo et al (2013), Badurally Adam et al (2015), and Ruhomally et al (2018), the models give rise to a recreational-addict free state, which may not always happen in reality. That is, it is not quite possible to have a population free of recreational users and addicts in a given society.…”

“…The aim of the present work is to propose a modified version of the model of Dauhoo et al (2013), Badurally Adam et al (2015) and Ruhomally et al (2018) by taking into account the social interactions that are responsible for the drug use spread within drug users community, which caters for the stochastic aspect of drug experimentation and drug addiction. A probabilistic cellular automaton (PCA) is set up by local transition rules that are capable of describing the social interactions and influences among both nonusers and drug users in a given population.…”

“…It needs to stressed that these rules mimic the dynamics of illicit drug use in a population. Moreover, in this model, birth and death processes are not taken into account, and thus, a constant population is considered in this system (Dauhoo et al 2013;Badurally Adam et al 2015;Ruhomally et al 2018).…”

A graph cellular automaton with relation-based neighbourhood describing the impact of peer influence on the consumption of marijuana among college-aged youths

“…Mathematical modelling of illicit drug consumption. The dynamical study of this social issue can be found in [1], [3], [7], [11], [12], [21], [25] and [23]. However, it must be pointed out that in all these works, the dynamics of the evolution of consumption of illicit drug, under the influence of the social interactions, which are responsible for the drug use spread within drug users community has not been taken into account.…”