scholarly journals Mathematical Modeling of the Impact of Rehabilitation Centers on Illicit Drug Usage

2021 ◽  
Author(s):  
Isa Baba ◽  
Saudatu Baba Sambo
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Global Stability ◽  
Numerical Simulations ◽  
Drug Users ◽  
Illicit Drug ◽  
Endemic Equilibrium ◽  
Drug Usage ◽  
Rehabilitation Centers ◽  
The Impact

Abstract This paper presents a mathematical model that studies the importance of treatment at rehabilitation centers intending to show the impact of the rehabilitation centers in minimizing illicit drug usage. We consider the global stability of endemic equilibrium using the properties of Volterra-Lyapunov matrices. Numerical simulations were carried out to show the impact of rehabilitation centers on illicit drug users.

scholarly journals Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1272
Author(s):  
Fengsheng Chien ◽  
Stanford Shateyi
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Global Stability ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Disease Model ◽  
Transmission Dynamics ◽  
Global Stability Analysis ◽  
Lyapunov Stability Analysis ◽  
Disease Free

This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.

scholarly journals The Deterministic Evolution Of Illicit Drug Consumption Within a Given Population

2018 ◽  
Vol 62 ◽  
pp. 139-157 ◽  
Author(s):  
Yusra Bibi Ruhomally ◽  
Nabeelah Banon Jahmeerbaccus ◽  
Muhammad Zaid Dauhoo
Keyword(s):  
Drug Users ◽  
Illicit Drug ◽  
Drug Consumption ◽  
Dynamic Evolution ◽  
Evidence Based ◽  
Relative Importance ◽  
Epidemic Threshold ◽  
Drug Usage ◽  
Policy Makers ◽  
Reproduction Numbers

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.

PARENTAL DRUG USAGE: EFFECT UPON CHROMOSOMES OF PROGENY

PEDIATRICS ◽  
1971 ◽  
Vol 47 (6) ◽  
pp. 1037-1041
Author(s):  
Kenneth W. Dumars
Keyword(s):  
Drug Users ◽  
Illicit Drugs ◽  
Illicit Drug ◽  
Medical Problem ◽  
Clinical State ◽  
Chromosomal Breakage ◽  
Drug Usage ◽  
Illicit Drug Users ◽  
Significant Difference

Illicit drug usage is a serious medical problem. Parental use of LSD and the effect upon the unborn infant is in question. However, parental use of LSD has often prevented acceptance of those children subsequently relinquished for adoption. In this study we reviewed the records and clinical state of over 1,000 consecutive infants who were relinquished for adoption. Clinical and developmental examination was conducted upon 47 and chromosomal karyotyping upon 41/47 infants whose parents were illicit drug users. In comparison with comparable controls we found no statistically significant difference in the incidence of chromosomal breakage or rearrangement. Parental use of illicit drugs does not in itself constitute a valid reason for the refusal to accept or place an infant relinquished for adoption.

scholarly journals Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students

2020 ◽  
Vol 16 (32) ◽  
pp. 195-223
Author(s):  
Edgardo Pérez
Keyword(s):  
Mathematical Modeling ◽  
College Students ◽  
Mathematical Model ◽  
Drinking Behavior ◽  
Preventive Measure ◽  
Nonlinear Mathematical Model ◽  
Consumption Behavior ◽  
Existence And Stability ◽  
Drugs And Crime ◽  
The Impact

In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.

Assessing the impact of agrochemicals on schistosomiasis transmission: A mathematical study

2021 ◽  
pp. 2150049
Author(s):  
Liming Cai ◽  
Peixia Yue ◽  
Mini Ghosh ◽  
Xuezhi Li
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Agricultural Pollution ◽  
Parasitic Disease ◽  
Mathematical Study ◽  
Proposed Model ◽  
Existence And Stability ◽  
The Impact

Schistosomiasis is a snail-borne parasitic disease, which is affecting almost 240 million people worldwide. The number of humans affected by schistosomiasis is continuously increasing with the rise in the use of agrochemicals. In this paper, a mathematical model is formulated and analyzed to assess the effect of agrochemicals on the transmission of schistosomiasis. The proposed model incorporates the effects of fertilizers, herbicides and insecticides on susceptible snails and snail predators along with schistosomiasis disease transmission. The existence and stability of the equilibria in the model are discussed. Sensitivity analysis is performed to identify the key parameters of the proposed model, which contributes most in the transmission of this disease. Numerical simulations are also performed to assess the impact of fertilizers, herbicides and insecticides on schistosomiasis outbreaks. Our study reveals that the agricultural pollution can enhance the transmission intensity of schistosomiasis, and in order to prevent the outbreak of schistosomiasis, the use of pesticides should be controlled.

scholarly journals Analysis of HIV Transmission of Commercial Sex Wokers and Their Clients with Condom Use Treatment

2019 ◽  
Vol 125 ◽  
pp. 05003 ◽  
Author(s):  
Sutimin ◽  
Siti Khabibah ◽  
Dita Anies Munawwaroh ◽  
R. Heri Soelistyo U
Keyword(s):  
Condom Use ◽  
Global Stability ◽  
Sex Workers ◽  
Hiv Transmission ◽  
Equilibrium States ◽  
Endemic Equilibrium ◽  
Reproduction Ratio ◽  
Aids Epidemic ◽  
The Impact ◽  
Hiv Aids

A model of the HIV/AIDS epidemic among sex workers and their clients is discussed to study the effects of condom use in the prevention of HIV transmission. The model is addressed to determine the existence of equilibrium states, and then analyze the global stability of disease free and endemic equilibrium states. The global stability of equilibria depends on the vales of the basic reproduction ratio derived from the next generation matrix of the model. The endemic equilibrium state is globally stable when the ratio exceeds unity. The simulation results are presented to discuss the effect of condom use treatment in preventing the spread of HIV/AIDS among sex workers and their clients. The results show that the effectiveness level in using condoms in sexual intercourse corresponds to the decreasing level of the spread of HIV/AIDS. We use Maple and Matlab software to simulate the impact of condom use.

scholarly journals Nonlinear Analysis of the Dynamics of Criminality and Victimisation: A Mathematical Model with Case Generation and Forwarding

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Chikodili Helen Ugwuishiwu ◽  
D. S. Sarki ◽  
G. C. E. Mbah
Keyword(s):  
Mathematical Model ◽  
Numerical Simulations ◽  
Nonlinear Analysis ◽  
Deterministic Model ◽  
Positive Impact ◽  
Threshold Value ◽  
Dynamical Analysis ◽  
Viable Option ◽  
Effective Implementation ◽  
The Impact

In this paper, a system of deterministic model is presented for the dynamical analysis of the interactional consequence of criminals and criminality on victimisation under two distinguishable forms of rehabilitation—the behavioural reformation of criminals and the emotional psychotherapy of victims. A threshold value, R0=maxRK,RV, responsible for the persistence of crime/criminality and victimisation, is obtained and, using it, stability analyses on the model performed. The impact of an effective implementation of the two forms of rehabilitation was found to be substantial on crime and criminality, while an ineffective implementation of same was observed to have a detrimental consequence. The prevention of repeat victimisation was seen to present a more viable option for containing crime than the noncriminalisation of victims. Further, the removal of criminals, either through quitting or death, among others, was also found to have a huge positive impact. Numerical simulations were performed for a variety of mixing criminal scenarios to verify the analytical results obtained.

scholarly journals An Approach for the Global Stability of Mathematical Model of an Infectious Disease

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1778
Author(s):  
Mojtaba Masoumnezhad ◽  
Maziar Rajabi ◽  
Amirahmad Chapnevis ◽  
Aleksei Dorofeev ◽  
Stanford Shateyi ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Global Stability ◽  
Incidence Rates ◽  
Endemic Equilibrium ◽  
Symmetry Properties ◽  
Nonlinear Incidence Rates ◽  
Lyapunov Matrix ◽  
The Stability ◽  
The Mathematical Model

The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra–Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra–Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The results developed in this paper can be applied in more complex systems with nonlinear incidence rates. Numerical simulations are presented to illustrate the analytical results.

scholarly journals Global Dynamics of a Mathematical Model on Smoking

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zainab Alkhudhari ◽  
Sarah Al-Sheikh ◽  
Salma Al-Tuwairqi
Keyword(s):  
Mathematical Model ◽  
Global Stability ◽  
Numerical Simulations ◽  
The Other ◽  
Global Dynamics ◽  
Local And Global Stability ◽  
Two Equilibria

We derive and analyze a mathematical model of smoking in which the population is divided into four classes: potential smokers, smokers, temporary quitters, and permanent quitters. In this model we study the effect of smokers on temporary quitters. Two equilibria of the model are found: one of them is the smoking-free equilibrium and the other corresponds to the presence of smoking. We examine the local and global stability of both equilibria and we support our results by using numerical simulations.

scholarly journals ECONOMIC AND MATHEMATICAL MODELING OF INVESTMENT ATTRACTIVENESS OF CONSTRUCTION ENTERPRISES IN THE SYSTEM OF STAKEHOLDER RELATIONS

2020 ◽  
Vol 6 (4) ◽  
pp. 56-65
Author(s):  
Volodymyr Velychko ◽  
Evgeniy Grytskov ◽  
Dmytriy Prunenko
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
External Control ◽  
Construction Enterprise ◽  
Stakeholder Relations ◽  
Construction Enterprises ◽  
Construction Companies ◽  
Quantitative Basis ◽  
Sound Management ◽  
The Impact

The relevance of the process of implementation of economic and mathematical model of investment attractiveness of the construction enterprise in the stakeholder relation system is proved. The results of the analysis of the theoretical provisions for determining investment attractiveness and stakeholders of construction enterprises are presented. An economic and mathematical model for the formation of stakeholder groups in the system of relations with construction enterprises is proposed. A system of information and analytical support for an integrated assessment of the level of stakeholder relations and investment attractiveness of construction enterprises has been formed, which creates the basis for economic and mathematical modeling. The directions, methods, and models for assessing investment attractiveness and the level of stakeholder relations of construction enterprises are proposed. The practical aspects of their implementation are determined. The results of economic and mathematical modeling of the investment attractiveness of construction enterprises in the system of stakeholder relations are presented. The subject of the research is the directions of formation and realization of economic and mathematical modeling of investment attractiveness of enterprises in the system of stakeholder relations. The formation of the research methodology is carried out on the basis of the theoretical and methodological platform for determining the investment attractiveness of enterprises and stakeholders that interact in the relevant field. In addition, a set of methods is used to conduct the study: analytical (to determine indicators of investment attractiveness); expert assessments (to determine the index of stakeholder relations); method of analysis of hierarchies (to assess the importance of the impact of stakeholders (customers of construction products; workers of construction enterprises; top management; managers of various levels of construction enterprises; owners of construction enterprises; government bodies influencing the formation and level of interaction of stakeholders with construction enterprises; public organizations influencing activities in construction and architecture; corporate governance bodies of construction enterprises; the bodies of internal and external control interacting in the construction industry; the competitors of construction enterprises; the suppliers of inventories interacting with construction enterprises; stakeholders interacting in the formation and use of spatial, urban, environmental information and creating investment attractiveness of construction enterprises; the design organizations; other stakeholders interacting with construction enterprises) at the level of stakeholders from noses of enterprises); economic and mathematical modeling (to establish causal links between the level of stakeholder relations and the index of investment attractiveness of enterprises); generalization and systematization (to obtain and interpret research results). The aim of the study is to establish causal relationships between the factors that shape the level of stakeholder relations and investment attractiveness of construction companies based on economic and mathematical tools. The result of the study is the formation of a quantitative basis for making sound management decisions in the system of stakeholder relations of construction companies to increase their investment attractiveness.

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