scholarly journals Dynamics and optimal control of an online game addiction model with considering family education

2021 ◽  
Vol 7 (3) ◽  
pp. 3745-3770
Author(s):  
Youming Guo ◽  
◽  
Tingting Li ◽  
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Rank Correlation ◽  
Latin Hypercube Sampling ◽  
Control Measures ◽  
Family Education ◽  
Online Game ◽  
Optimal Control Strategy ◽  
Game Addiction ◽  
Existence And Stability

<abstract><p>The problem of online game addiction among teenagers is becoming more and more serious in many parts of the world. Many of them are addicted to online games due to the lack of family education, which is an important factor that can not be ignored. To explore the optimal strategy for controlling the spread of game addiction, a new dynamic model of teenagers' online game addiction with considering family education is developed. Firstly, we perform a qualitative dynamic analysis of the model. We study the nonnegativity and boundedness of solutions, the basic reproduction number $ R_{0} $, and the existence and stability of equilibria. We then consider a model with control measures of family education, isolation and treatment, and obtain the expression of optimal control. In the numerical simulation, we study the global sensitivity analysis by the combination of Latin Hypercube Sampling (LHS) and partial rank correlation coefficient (PRCC) techniques, and show the relationship between $ R_{0} $ and each parameter. Then the forward backward sweep method with fourth order Runge-Kutta is used to simulate the control strategy in each scenario. Finally, the optimal control strategy is obtained by comparing incremental cost-effectiveness ratio (ICER) and infection averted ratio (IAR) under all strategies. The results show that with sufficient financial resources, adding the family education measures can help more teenagers avoid being addicted to games and control the spread of game addiction more effectively.</p></abstract>

scholarly journals Stability and optimal control in a mathematical model of online game addiction

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5691-5711 ◽  
Author(s):  
Tingting Li ◽  
Youming Guo
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Maximum Principle ◽  
Control Strategy ◽  
Reproduction Number ◽  
Direct Transfer ◽  
Online Game ◽  
Optimal Control Strategy ◽  
Game Addiction ◽  
The Basic Reproduction Number

In this paper, we construct an online game addiction model(including susceptible, infective, professional and quitting compartments). We also consider that the direct transfer from the susceptible individuals to the professional individuals. Some properties of the model are derived by the basic reproduction number R0 and stability of all kinds of equilibria is obtained. Then we use Pontriagin?s maximum principle to solve the optimal control strategy. Finally, Numerical simulations are also conducted in the analytic results.

scholarly journals Modeling the Impact of Optimal Control Strategies on the Dynamics of Zika Virus Disease Using the Sterile Insect Technology

2020 ◽  
pp. 13-33
Author(s):  
Atokolo William ◽  
Akpa Johnson ◽  
Daniel Musa Alih ◽  
Olayemi Kehinde Samuel ◽  
C. E. Mbah Godwin
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Zika Virus ◽  
Human Population ◽  
Necessary Conditions ◽  
Virus Disease ◽  
Control Strategies ◽  
Control Measures ◽  
Optimal Control Strategy ◽  
The Impact

This work is aimed at formulating a mathematical model for the control of zika virus infection using Sterile Insect Technology (SIT). The model is extended to incorporate optimal control strategy by introducing three control measures. The optimal control is aimed at minimizing the number of Exposed human, Infected human and the total number of Mosquitoes in a population and as such reducing contacts between mosquitoes and human, human to human and above all, eliminates the population of Mosquitoes. The Pontryagin’s maximum principle was used to obtain the necessary conditions, find the optimality system of our model and to obtain solution to the control problem. Numerical simulations result shows that; reduction in the number of Exposed human population, Infected human population and reduction in the entire population of Mosquito population is best achieved using the optimal control strategy.

scholarly journals Optimal Control Techniques on a Mathematical Model for the Dynamics of Tungiasis in a Community

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Jairos Kahuru ◽  
Livingstone S. Luboobi ◽  
Yaw Nkansah-Gyekye
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Strategy ◽  
Control Strategies ◽  
Control Process ◽  
Control Measures ◽  
Human Beings ◽  
Optimal Control Strategy ◽  
Control Techniques ◽  
Existence Of Optimal Control

Tungiasis is a permanent penetration of female sand flea“Tunga penetrans”into the epidermis of its host. It affects human beings and domestic and sylvatic animals. In this paper, we apply optimal control techniques to a Tungiasis controlled mathematical model to determine the optimal control strategy in order to minimize the number of infested humans, infested animals, and sand flea populations. In an attempt to reduce Tungiasis infestation in human population, the control strategies based on personal protection, personal treatment, educational campaign, environmental sanitation, and insecticidal treatments on the affected parts as well as on animal fur are considered. We prove the existence of optimal control problem, determine the necessary conditions for optimality, and then perform numerical simulations. The numerical results showed that the control strategy comprises all five control measures and that which involves the three control measures of insecticide control, insecticidal dusting on animal furs, and environmental hygiene has the significant impact on Tungiasis transmission. Therefore, fighting against Tungiasis infestation in endemic settings, multidimensional control process should be employed in order to achieve the maximum benefits.

scholarly journals Dynamic modeling and optimal control of cystic echinococcosis

2021 ◽  
Author(s):  
Xinmiao Rong ◽  
Meng Fan ◽  
Huaiping Zhu ◽  
Yaohui Zheng
Keyword(s):  
Optimal Control ◽  
Numerical Simulations ◽  
Control Strategy ◽  
Cystic Echinococcosis ◽  
Control Measures ◽  
Domestic Dog ◽  
Contour Plot ◽  
Control Cost ◽  
Optimal Control Strategy ◽  
Stray Dogs

Abstract Background: Cystic echinococcosis is one of the most severe helminth zoonosis with a drastic impact on human health and livestock industry. Investigating optimal control strategy and assessing the crucial factors are essential for developing countermeasures to mitigate this disease.Methods: Two compartment models were formulated to study the dynamics of cystic echinococcosis transmission, to evaluate the effectiveness of various control measures, and to find the optimal control strategy. Sensitive analyses were conducted by obtaining PRCCs and contour plot was used to evaluate the effect of key parameters on the basic reproduction number. Based on forward-backward sweep method, numerical simulations were employed to investigate effects of key factors on the transmission of cystic echinococcosis and to obtain the optimal control strategy.Results: The food resources of stray dog and invalid sheep vaccination rate, which are always neglected, were significant to the transmission and control of cystic echinococcosis. Numerical simulations suggest that, the implementation of optimal control strategy can significantly reduce the infections. Improving the cost of health education and domestic dog deworming could not decrease human infections.Conclusions: Our study showed that only a long-term use of the optimal control measures can eliminate the disease. Meanwhile, during the intervention, sheep vaccination and stray dogs disposing should be emphasized ahead of domestic dogs deworming to minimize the control cost. Simultaneously reducing other wild intermediate hosts and strengthening the sheep vaccination as well as disposing the stray dogs would be most effective.

scholarly journals Dynamic modeling and optimal control of cystic echinococcosis

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Xinmiao Rong ◽  
Meng Fan ◽  
Huaiping Zhu ◽  
Yaohui Zheng
Keyword(s):  
Optimal Control ◽  
Numerical Simulations ◽  
Control Strategy ◽  
Cystic Echinococcosis ◽  
Control Measures ◽  
Domestic Dog ◽  
Contour Plot ◽  
Control Cost ◽  
Optimal Control Strategy ◽  
Stray Dogs

Abstract Background Cystic echinococcosis is one of the most severe helminth zoonosis with a drastic impact on human health and livestock industry. Investigating optimal control strategy and assessing the crucial factors are essential for developing countermeasures to mitigate this disease. Methods Two compartment models were formulated to study the dynamics of cystic echinococcosis transmission, to evaluate the effectiveness of various control measures, and to find the optimal control strategy. Sensitive analyses were conducted by obtaining PRCCs and contour plot was used to evaluate the effect of key parameters on the basic reproduction number. Based on forward–backward sweep method, numerical simulations were employed to investigate effects of key factors on the transmission of cystic echinococcosis and to obtain the optimal control strategy. Results The food resources of stray dog and invalid sheep vaccination rate, which are always neglected, were significant to the transmission and control of cystic echinococcosis. Numerical simulations suggest that, the implementation of optimal control strategy can significantly reduce the infections. Improving the cost of health education and domestic dog deworming could not decrease human infections. Conclusions Our study showed that only a long-term use of the optimal control measures can eliminate the disease. Meanwhile, during the intervention, sheep vaccination and stray dogs disposing should be emphasized ahead of domestic dogs deworming to minimize the control cost. Simultaneously reducing other wild intermediate hosts and strengthening the sheep vaccination as well as disposing the stray dogs would be most effective.

scholarly journals Dynamic Modeling and Optimal Control of Cystic Echinococcosis

2020 ◽  
Author(s):  
Xinmiao Rong ◽  
Meng Fan ◽  
Huaiping Zhu
Keyword(s):  
Optimal Control ◽  
Numerical Simulations ◽  
Control Strategy ◽  
Cystic Echinococcosis ◽  
Control Measures ◽  
Domestic Dog ◽  
Contour Plot ◽  
Control Cost ◽  
Optimal Control Strategy ◽  
Stray Dogs

Abstract Background: Cystic echinococcosis is one of the most severe helminth zoonosis with a drastic impact on human health and livestock industry. Investigating optimal control strategy and assessing the crucial factors are essential for developing countermeasures to mitigate this disease. Methods: Two compartment models were formulated to study the dynamics of cystic echinococcosis transmission, to evaluate the effectiveness of various control measures, and to find the optimal control strategy. Sensitive analyses were conducted by obtaining PRCCs and contour plot were used to evaluate the effect of key parameters on the basic reproduction number. Based on forward-backward sweep method, numerical simulations were employed to investigate effects of key factors on the transmission of cystic echinococcosis and to obtain the optimal control strategy. Results: The food resources of stray dog and invalid sheep vaccination rate, which are always neglected, were significant to the transmission and control of cystic echinococcosis. Numerical simulations suggest that, the implementation of optimal control strategy can significantly reduce the infections. Improving the cost of health education and domestic dog deworming could not decrease human infections. Conclusions: Our study showed that only a long-term use of the optimal control measures can eliminate the disease. Meanwhile, during the intervention, sheep vaccination and stray dogs disposing should be emphasized ahead of domestic dogs deworming to minimize the control cost. Simultaneously reducing other wild intermediate hosts and strengthening the sheep vaccination as well as disposing the stray dogs would be most effective.

Mathematical Analysis of an Epidemic System in the Presence of Optimal Control and Population Dispersal

2018 ◽  
Vol 13 (01) ◽  
pp. 1-17 ◽  
Author(s):  
Swapan Kumar Nandi ◽  
Soovoojeet Jana ◽  
Manotosh Mandal ◽  
T. K. Kar
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Sexually Transmitted Diseases ◽  
Control Strategy ◽  
Control Parameters ◽  
Stability Criteria ◽  
Optimal Control Strategy ◽  
Sexually Transmitted ◽  
Existence And Stability ◽  
Theoretical Results

In this paper, we proposed and analyzed a susceptible-infected-recovered (SIR) type epidemic model to investigate the effect of transport-related infectious diseases namely tuberculosis, measles, rubella, influenza, sexually transmitted diseases, etc. The existence and stability criteria of both the diseases include free equilibrium point and endemic equilibrium point which are established and the threshold parametric condition for which the system passes through a transcritical bifurcation is also obtained. Optimal control strategy for control parameters is formulated and solved both theoretically and numerically. Lastly, we not only illustrate our theoretical results through graphical illustrations but also computer simulation is used to show that our model would be a good model to study the SARS epidemic in 2003.

Application of Optimal Control Strategy to Converter Gas Recovery System

2012 ◽  
Vol 38 (6) ◽  
pp. 1017 ◽  
Author(s):  
Jia-Yan ZHANG ◽  
Zhong-Hai MA ◽  
Xiao-Bin QIAN ◽  
Shao-Ming LI ◽  
Jia-Hong LANG
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Optimal Control Strategy ◽  
Gas Recovery ◽  
Recovery System ◽  
Converter Gas
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