Mathematical Modelling on the Effects of Drug Abuse to the Societies

Matonya, Fikiri Lucas; Kuznetsov, D.V.

doi:10.22457/apam.591v19n1a4

Cited by 3 publications

(4 citation statements)

References 10 publications

(14 reference statements)

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“…Sensitivity analysis is the process performed when we want to determine the influence of each model parameter in the effective reproduction number 0 R [25,26]. Thus, this process helps in the selection of corruption control measures in which the most sensitive parameters are seriously considered.…”

Section: The Effective Reproduction Number Sensitivity Analysis and Their Analytical Interpretationmentioning

confidence: 99%

“…Considering the most negative sensitivity indices which are α , β and d µ . From Table 3, corruption induced death rate d µ is the most negative sensitivity parameter but we will not recommend as one of the controls of corruption because it is against human right and unethical to increase corruption induced death rate [26]. Therefore, we consider the rest two parameters of mass education α and religious teaching β .…”

Section: The Effective Reproduction Number Sensitivity Analysis and Their Analytical Interpretationmentioning

confidence: 99%

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Mathematical Modelling and Analysis of Corruption Dynamics with Control Measures in Tanzania

Danford¹,

Kimathi²,

Mirau³

2020

J. Math. Inf.

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Corruption is a worldwide problem that affects many countries where by individuals loses their rights, lower community confidence in public authorities, absence of peace and security, misallocation of resources and termination of employment. Despite various measures which have been taken by various countries to control corruption, the problem still exists. In this paper, we formulate and analyze a mathematical model for the dynamics of corruption in the presence of control measures. Analysis of the model shows that both Corruption Free Equilibrium (CFE) and Corruption Endemic Equilibrium (CEE) exist. The next generation matrix method was used to compute the effective reproduction number (ܴ ) which is used to study the corruption dynamics. The results indicate that CFE is both locally and globally asymptotically stable when ܴ < 1 whereas CEE is globally asymptotically stable when ܴ > 1. The normalized forward sensitivity method was used to describe the most sensitive parameters for the spread of corruption. The most positive sensitive parameters are κ and ν while the most negative sensitive parameters are α and β . Therefore, the parameters of mass education α and religious teaching β are the best parameters for control of corruption. The model was simulated using Runge-Kutta fourth order method in MATLAB and the results indicate that the combination of mass education and religious teaching is effective to corruption control within short time compared to when each control strategy is used separately. Therefore, this study recommends that more efforts in providing both mass education and religious teaching should be applied at the same time to control corruption.

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Section: The Effective Reproduction Number Sensitivity Analysis and Their Analytical Interpretationmentioning

confidence: 99%

Section: The Effective Reproduction Number Sensitivity Analysis and Their Analytical Interpretationmentioning

confidence: 99%

Mathematical Modelling and Analysis of Corruption Dynamics with Control Measures in Tanzania

Danford¹,

Kimathi²,

Mirau³

2020

J. Math. Inf.

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“…In other words, it can be defined as excessive use of or dependence on any psychoactive chemical substance to establish harmful effects on users' physical, social, psychological, and mental health. According to recent studies conducted by [1,2,3,4], some drug users get initiated through prescription rather than experimentation and later misuse the opportunity. In the works of [5,6,7], the results revealed that public tolerance of drug usage, with limited consideration of the adverse health and socio-economic consequences can influence initiation as well as continuous usage.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling of Illicit Drug Use Dynamics Examining the Impact of Recycling Recovered Individuals into the Population.

Rwat Solomon Isa,

Sabastine Emmanuel,

Nanle Tanko Danat

et al. 2024

AMCI

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Illicit drug use continues to pose a significant threat to public health and societal well-being. This study aims to develop a comprehensive mathematical model that captures the dynamics of illicit drug use, considering different categories such as susceptible individuals, exposed individuals, drug addicts, and individuals in recovery. The model accounts for the fact that recovered individuals may not develop lifelong resistance to drugs and that those exposed to drug use cannot introduce new individuals into drug usage. Through the mathematical model, we seek to enhance our understanding of the behavior and patterns of illicit drug use, contributing valuable insights to the field of drug-related research. Additionally, the study explores the properties of the proposed model and utilizes the next generation matrix method to calculate the effective reproduction number. Furthermore, a sensitivity analysis is conducted to evaluate the impact of various parameters on the reproduction number, identifying the most effective control measures for mitigating the spread of drug-induced issues. The findings of this study serve as a warning indication to individuals and governments, emphasizing the need to intensify efforts in combating drug abuse. Moreover, the study highlights the importance of considering backward or forward bifurcation phenomena in determining the local stability of the model system at the endemic equilibrium point. This research contributes to the ongoing efforts to understand and address the complex challenges posed by illicit drug use, offering insights that can inform policies and interventions aimed at curbing the spread of drug abuse and promoting overall community well-being.

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“…In this paper, we consider a simple mathematical model with a system of ordinary differential equations for the population dynamics about the internet gaming, especially focusing on the social nature of online gaming which would be regarded as a factor to reinforce the transition to the addictive gaming. Although our mathematical model may seem to be an application of some models about the transmission of infectious disease like the previous models on the addition (see, for example, [9,16,29] on the online gaming addiction, [2,20] on the drug addiction), such an introduction of the effect from the social nature of online gaming in the population dynamics makes the mathematical model distinctive from that for the epidemic dynamics of a transmissible disease (as for the mathematical modeling and models about the epidemic dynamics, for example, see [5,10,13,19]). Further, our model is not on the state transition of individual who are craving to play the online game, for example, like that by [6], but it is on an epidemiological dynamics of addictive gamers in a community.…”

Section: Introductionmentioning

confidence: 99%

A mathematical model of population dynamics for the internet gaming addiction

Seno

2021

NAMC

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As the number of internet users appears to steadily increase each year, Internet Gaming Disorder (IGD) is bound to increase as well. The question how this increase will take place, and what factors have the largest impact on this increase, naturally arises. We consider a system of ordinary differential equations as a simple mathematical model of the population dynamics about the internet gaming. We assume three stages about the internet gamer’s state: moderate, addictive, and under treatment. The transition of the gamer’s state between the moderate and the addictive stages is significantly affected by the social nature of internet gaming. As the activity of social interaction gets higher, the gamer would be more likely to become addictive. With the inherent social reinforcement of internet game, the addictive gamer would hardly recontrol his/herself to recover to the moderate gamer. Our result on the model demonstrates the importance of earlier initiation of a system to check the IGD and lead to some medical/therapeutic treatment. Otherwise, the number of addictive gamers would become larger beyond the socially controllable level.

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Mathematical Modelling on the Effects of Drug Abuse to the Societies

Cited by 3 publications

References 10 publications

Mathematical Modelling and Analysis of Corruption Dynamics with Control Measures in Tanzania

Mathematical Modelling and Analysis of Corruption Dynamics with Control Measures in Tanzania

Mathematical Modeling of Illicit Drug Use Dynamics Examining the Impact of Recycling Recovered Individuals into the Population.

A mathematical model of population dynamics for the internet gaming addiction

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