scholarly journals Modelling the Influence of Awareness Programs by Media on the Drinking Dynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hai-Feng Huo ◽  
Qian Wang
Keyword(s):  
Mathematical Model ◽  
Sufficient Conditions ◽  
Alcohol Problems ◽  
Behavioral Changes ◽  
Nonlinear Mathematical Model ◽  
Effective Measure ◽  
Heavy Drinkers ◽  
Awareness Programs ◽  
The Stability ◽  
Separate Class

We develop a nonlinear mathematical model with the effect of awareness programs on the binge drinking. Due to the fact that awareness programs are capable of inducing behavioral changes in nondrinkers, we introduce a separate class by avoiding contacts with the heavy drinkers. Furthermore we assume that cumulative density of awareness programs increases at a rate proportional to the number of heavy drinkers. We establish some sufficient conditions for the stability of the alcohol free and the alcohol present equilibria and give some numerical simulations to explain our main result. Our results show that awareness programs is an effective measure in reducing alcohol problems.

EFFECT OF AWARENESS PROGRAMS IN CONTROLLING THE PREVALENCE OF AN EPIDEMIC WITH TIME DELAY

2011 ◽  
Vol 19 (02) ◽  
pp. 389-402 ◽  
Author(s):  
A. K. MISRA ◽  
ANUPAMA SHARMA ◽  
VISHAL SINGH
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Stability Theory ◽  
Direct Contact ◽  
Behavioral Changes ◽  
Nonlinear Mathematical Model ◽  
Awareness Programs

A nonlinear mathematical model with delay to capture the dynamics of effect of awareness programs on the prevalence of any epidemic is proposed and analyzed. It is assumed that pathogens are transmitted via direct contact between susceptibles and infectives. It is assumed further that cumulative density of awareness programs increases at a rate proportional to the number of infectives. It is considered that awareness programs are capable of inducing behavioral changes in susceptibles, which result in the isolation of aware population. The model is analyzed using stability theory of differential equations and numerical simulations. The model analysis shows that, though awareness programs cannot eradicate infection, they help in controlling the prevalence of disease. It is also found that time delay in execution of awareness programs destabilizes the system and periodic solutions may arise through Hopf-bifurcation.

A Mathematical Model for the Control of Infectious Diseases: Effects of TV and Radio Advertisements

2018 ◽  
Vol 28 (03) ◽  
pp. 1850037 ◽  
Author(s):  
A. K. Misra ◽  
Rajanish Kumar Rai
Keyword(s):  
Mathematical Model ◽  
Infectious Diseases ◽  
Behavioral Changes ◽  
Control Mechanisms ◽  
Cumulative Number ◽  
Nonlinear Mathematical Model ◽  
Model Formulation ◽  
Infection Period ◽  
Awareness Programs ◽  
Precautionary Measures

The broadcast of awareness programs through TV and radio advertisements (ads) makes people aware and brings behavioral changes among the individuals regarding the risk of infection and its control mechanisms. In this paper, we propose and analyze a nonlinear mathematical model for the control of infectious diseases due to impact of TV and radio advertisements. It is assumed that susceptible individuals are vulnerable to infection as well as information through TV and radio ads and they contract infection via direct contact with infected individuals. In the model formulation, it is also assumed that the growth rates in cumulative number of TV and radio ads are proportional to the number of infected individuals with decreasing function of aware individuals. Further, it is assumed that awareness among susceptible individuals induces behavioral changes and they form separate aware classes, which are fully protected from infection as they use precautionary measures for their protection during the infection period. The feasibility of equilibria and their stability properties are discussed. It is shown that the augmentation in dissemination rate of awareness among susceptible individuals due to TV and radio ads may cause stability switches through Hopf-bifurcation. The analytical findings are supported through numerical simulations.

scholarly journals A stochastic mathematical model of two different infectious epidemic under vertical transmission

2021 ◽  
Vol 19 (3) ◽  
pp. 2179-2192
Author(s):  
Xunyang Wang ◽  
◽  
Canyun Huang ◽  
Yixin Hao ◽  
Qihong Shi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Vertical Transmission ◽  
Biological Significance ◽  
Sufficient Conditions ◽  
Discussion Section ◽  
Stochastic Permanence ◽  
Stochastic Epidemic ◽  
The Stability ◽  
Well Posed ◽  
Theoretical Results

<abstract><p>In this study, considering the effect of environment perturbation which is usually embodied by the alteration of contact infection rate, we formulate a stochastic epidemic mathematical model in which two different kinds of infectious diseases that spread simultaneously through both horizontal and vertical transmission are described. To indicate our model is well-posed and of biological significance, we prove the existence and uniqueness of positive solution at the beginning. By constructing suitable $ Lyapunov $ functions (which can be used to prove the stability of a certain fixed point in a dynamical system or autonomous differential equation) and applying $ It\hat{o} $'s formula as well as $ Chebyshev $'s inequality, we also establish the sufficient conditions for stochastic ultimate boundedness. Furthermore, when some main parameters and all the stochastically perturbed intensities satisfy a certain relationship, we finally prove the stochastic permanence. Our results show that the perturbed intensities should be no greater than a certain positive number which is up-bounded by some parameters in the system, otherwise, the system will be surely extinct. The reliability of theoretical results are further illustrated by numerical simulations. Finally, in the discussion section, we put forward two important and interesting questions left for further investigation.</p></abstract>

scholarly journals A Comparative Study Between Two Systems with and Without Awareness in Controlling HIV/AIDS

2017 ◽  
Vol 27 (2) ◽  
pp. 337-350 ◽  
Author(s):  
Shubhankar Saha ◽  
Priti Kumar Roy
Keyword(s):  
Antiretroviral Treatment ◽  
Reproduction Number ◽  
Health Planning ◽  
Hiv Infections ◽  
Nonlinear Mathematical Model ◽  
Public Attention ◽  
Awareness Programs ◽  
The Stability ◽  
Hiv Aids

AbstractIt has always been a priority for all nations to reduce new HIV infections by implementing a comprehensive HIV prevention programme at a sufficient scale. Recently, the ‘HIV counselling & testing’ (HCT) campaign is gaining public attention, where HIV patients are identified through screening and immediately sent under a course of antiretroviral treatment (ART), neglecting the time extent they have been infected. In this article, we study a nonlinear mathematical model for the transmission dynamics of HIV/AIDS system receiving drug treatment along with effective awareness programs through media. Here, we consider two different circumstances: when treatment is only effective and when both treatment and awareness are included. The model is analyzed qualitatively using the stability theory of differential equations. The global stabilities of the equilibria under certain conditions are determined in terms of the model reproduction number. The effects of changes in some key epidemiological parameters are investigated. Projections are made to predict the long term dynamics of the disease. The epidemiological implications of such projections on public health planning and management are discussed. These studies show that the aware populations were less vulnerable to HIV infection than the unaware population.

Dynamics of the impact of Twitter with time delay on the spread of infectious diseases

2018 ◽  
Vol 11 (05) ◽  
pp. 1850067 ◽  
Author(s):  
Maoxing Liu ◽  
Yuting Chang ◽  
Haiyan Wang ◽  
Benxing Li
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Reproduction Number ◽  
Behavioral Changes ◽  
The Public ◽  
The Stability ◽  
The Impact ◽  
The Basic Reproduction Number

In this paper, a mathematical model to study the impact of Twitter in controlling infectious disease is proposed. The model includes the dynamics of “tweets” which may enhance awareness of the disease and cause behavioral changes among the public, thus reducing the transmission of the disease. Furthermore, the model is improved by introducing a time delay between the outbreak of disease and the release of Twitter messages. The basic reproduction number and the conditions for the stability of the equilibria are derived. It is shown that the system undergoes Hopf bifurcation when time delay is increased. Finally, numerical simulations are given to verify the analytical results.

Stochastic epidemic dynamics based on the association between susceptible and recovered individuals

2020 ◽  
pp. 2050085
Author(s):  
Luyao Xin ◽  
Yingxin Guo ◽  
Quanxin Zhu
Keyword(s):  
Mathematical Model ◽  
White Noise ◽  
Numerical Simulations ◽  
Sufficient Conditions ◽  
Deterministic Case ◽  
Epidemic Dynamics ◽  
Stochastic Epidemic ◽  
The Stability ◽  
Permanence In Mean ◽  
Theoretical Results

In this paper, we propose a new mathematical model based on the association between susceptible and recovered individual. Then, we study the stability of this model with the deterministic case and obtain the conditions for the extinction of diseases. Moreover, in view of the association between susceptible and recovered individual perturbed by white noise, we also give sufficient conditions for the extinction and the permanence in mean of disease with the white noise. Finally, we have numerical simulations to demonstrate the correctness of obtained theoretical results.

scholarly journals A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Bouchaib Khajji ◽  
Abderrahim Labzai ◽  
Abdelfatah Kouidere ◽  
Omar Balatif ◽  
Mostafa Rachik
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Addiction Treatment ◽  
Optimal Strategies ◽  
Optimal Controls ◽  
Optimization Strategy ◽  
Heavy Drinkers ◽  
Awareness Programs ◽  
Discrete Mathematical Model

In this paper, we propose a discrete mathematical model that describes the interaction between the classes of drinkers, namely, potential drinkers P, moderate drinkers M, heavy drinkers H, poor heavy drinkers Tp, rich heavy drinkers Tr, and quitters of drinking Q. We also focus on the importance of treatment within addiction treatment centers aiming to find the optimal strategies to minimize the number of drinkers and maximize the number of heavy drinkers who join addiction treatment centers. We use three controls which represent awareness programs through media and education for the potential drinkers, efforts to encourage the heavy drinkers to join addiction treatment centers, and psychological support with follow-up for the individuals who quit drinking. We use Pontryagin’s maximum principle in discrete time to characterize these optimal controls. The resulting optimality system is solved numerically by Matlab. Consequently, the obtained results confirm the performance of the optimization strategy.

A STUDY ON THE MATHEMATICAL MODEL FOR THE POPULATION AGE REPLACEMENT OF PINUS KORAIENSIS IN NATURAL FOREST

2010 ◽  
Vol 03 (01) ◽  
pp. 93-104
Author(s):  
XIAOJING WANG ◽  
GUOHUA SONG
Keyword(s):  
Mathematical Model ◽  
Limit Cycle ◽  
Sufficient Conditions ◽  
Natural Forest ◽  
Pinus Koraiensis ◽  
Positive Equilibrium ◽  
Korean Pine ◽  
The Stability ◽  
Age Replacement ◽  
The Mathematical Model

In this paper, a mathematical model for the population age replacement of Pinus koraiensis (Korean pine) in natural forest is developed. Using the stability and qualitative theory of ordinary differential equations, the sufficient conditions of existence of limit cycle and globally asymptotic stability of the positive equilibrium for the model are given. Furthermore, the stability of limit cycle is determined. At last we validate the result by plotting with Maple and conclude that young trees and mother trees of Pinus koraiensis in natural forest will change in a periodic undulation.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

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