scholarly journals Optimal Control of Rumor Spreading Model with Consideration of Psychological Factors and Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Liang’an Huo ◽  
Chenyang Ma
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Psychological Factors ◽  
Control Strategies ◽  
Information Age ◽  
Control Cost ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Official Information ◽  
Type Ii Functional Response

Rumors have rapidly increasing influence on the society as well as individual life in the information age. How to control the spread of such rumors effectively has become an urgent problem to be solved. In this paper, we consider an optimal control of rumor spreading model with psychological factors and time delay. Firstly, we introduce a realistic optimal control of rumor spreading model with consideration of Holling-type II functional response and time delay. Secondly, by introducing two control strategies of both promoting scientific knowledge and releasing official information, we formulate an optimal control problem to minimize both the number of ignorant individuals and spreaders and the control cost. Thirdly, we prove the existence and the necessary conditions of optimal control strategies theoretically based on Pontryagin’s maximum principle. Our results indicate that the proposed control strategies are effective in reducing the number of spreaders and ignorant individuals and minimizing control cost.

scholarly journals Dynamical analysis of a stochastic rumor-spreading model with Holling II functional response function and time delay

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liang’an Huo ◽  
Xiaomin Chen
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Functional Response ◽  
Response Function ◽  
Rapid Development ◽  
Dynamical Behavior ◽  
Deterministic System ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Holling Ii Functional Response

AbstractWith the rapid development of information society, rumor plays an increasingly crucial part in social communication, and its spreading has a significant impact on human life. In this paper, a stochastic rumor-spreading model with Holling II functional response function considering the existence of time delay and the disturbance of white noise is proposed. Firstly, the existence of a unique global positive solution of the model is studied. Then the asymptotic behavior of the global solution around the rumor-free and rumor-local equilibrium nodes of the deterministic system is discussed. Finally, through some numerical results, the validity and availability of theoretical analysis is verified powerfully, and it shows that some factors such as the transmission rate, the intensity of white noise, and the time delay have significant relationship with the dynamical behavior of rumor spreading.

A multi-delay model for pest control with awareness induced interventions — Hopf bifurcation and optimal control analysis

2020 ◽  
Vol 13 (06) ◽  
pp. 2050047
Author(s):  
Fahad Al Basir
Keyword(s):  
Optimal Control ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Time Delays ◽  
Control Strategies ◽  
Control Analysis ◽  
Agricultural Practice ◽  
Delay Model ◽  
Awareness Campaigns ◽  
Farming Awareness

Farming awareness is an important measure for pest controlling in agricultural practice. Time delay in controlling pest may affect the system. Time delay occurs in organizing awareness campaigns, also time delay may takes place in becoming aware of the control strategies or implementing suitable controlling methods informed through social media. Thus we have derived a mathematical model incorporating two time delays into the system and Holling type-II functional response. The existence and the stability criteria of the equilibria are obtained in terms of the basic reproduction number and time delays. Stability changes occur through Hopf-bifurcation when time delays cross the critical values. Optimal control theory has been applied for cost-effectiveness of the delayed system. Numerical simulations are carried out to justify the analytical results. This study shows that optimal farming awareness through radio, TV etc. can control the delay induced bifurcation in a cost-effective way.

Dynamical behaviors and spatial diffusion in a psychologically realistic rumor spreading model

2020 ◽  
Vol 31 (02) ◽  
pp. 2050034
Author(s):  
Yingying Cheng ◽  
Liang’an Huo ◽  
Liang Ma ◽  
Hongyuan Guo
Keyword(s):  
Psychological Factors ◽  
Cumulative Effect ◽  
Threshold Condition ◽  
Field Equations ◽  
Final Size ◽  
Dynamical Mechanism ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Mean Field Equations ◽  
Sensory Intensity

The spread of rumors has caused serious social and economic problems, especially during emergencies. Reducing the harm caused by rumors requires understanding the dynamical mechanism by which they propagate. To include the influence of time-dependent psychological factors, this paper proposes an improved rumor spreading model and derives mean-field equations describing the dynamics of rumor spreading. The psychological factors considered are the attenuation of individual interest, the cumulative effect of memory, and changes in sensory intensity with time. We also obtain the threshold condition of rumor spreading. Numerical simulations are used to verify our theoretical results. It is proved that the extremum of the cumulative effect of memory and the rumor attraction rate are positively correlated with the peak number of rumor spreaders, and negatively with the time required to reach the final rumor size. Time grows geometrically, while sensory intensity grows arithmetically. The initial approval rate of the memory accumulation effect and the stifling mechanism have little effect on the final rumor size. Finally, it is found that increasing the attenuation of interest coefficient reduces the time needed for the rumor to reach its final size.

Control strategies of avian influenza pandemic model with time delay

2017 ◽  
Vol 10 (07) ◽  
pp. 1750104 ◽  
Author(s):  
U. Roman ◽  
Z. Gul ◽  
I. Saeed ◽  
U. Hakeem ◽  
S. Shafie
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Avian Influenza ◽  
Control Strategies ◽  
Influenza Pandemic ◽  
Dynamical Behavior ◽  
Controlled System ◽  
Exponential Factor ◽  
Discrete Time Delay ◽  
Delay Differential

A mathematical model for avian influenza with optimal control strategies is presented as a system of discrete time delay differential equations (DDEs) and its important mathematical features are analyzed. In alignment to manage this, we develop an optimally controlled pandemic model of avian influenza and insert a time delay with exponential factor. Then we apply two controlled functions in the form of biosecurity of poultry and the education campaign against avian influenza to control the disperse of the disease. Our optimal control strategies will minimize the number of contaminated humans and contaminated birds. We also derive the basic reproduction number to examine the dynamical behavior of the model and demonstrate the existence of the controlled system. For the justification of our work, we present numerical simulations.

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