scholarly journals Optimal Control of ISTR Rumor Propagation Model with Social Reinforcement in Heterogeneous Network

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Liang’an Huo ◽  
Sijing Chen ◽  
Xiaoxiao Xie ◽  
Huiyuan Liu ◽  
Jianjia He
Keyword(s):  
Optimal Control ◽  
Reproduction Number ◽  
Control Strategies ◽  
Minimum Principle ◽  
Optimal Solution ◽  
Propagation Model ◽  
Social Reinforcement ◽  
Social Stability ◽  
Rumor Propagation ◽  
Rumor Control

The wide spread of rumor is undoubtedly harmful to social stability; we should try to lower the effect of rumor on society. Therefore, it is reasonable to put forward the rumor control strategy on the basis of the study of the law of rumor propagation. Firstly, the ISTR model of rumor is established by including influencing factors of true information spreader and social reinforcement. And by using the next generation matrix method, the basic reproduction number of rumor is obtained. Then, in order to minimize the adverse effects of rumors, through introducing two control strategies of scientific knowledge popularization and refutation of rumors, the optimal control problem is established. And through using Pontryagin’s Minimum Principle, the optimal solution of the rumor propagation model is solved. Finally, through theoretical analysis and numerical simulation, some results can be obtained. The results show that adding true information spreaders into the rumor model can effectively control the rumor propagation, and social reinforcement plays a significance role in rumor. The results also prove that these two control strategies can effectively inhibit the propagation of rumors. With the addition of control strategies, the number of true information spreaders increases, while the number of rumor spreaders decreases.

scholarly journals Optimal Control of a Dengue-Dengvaxia Model: Comparison Between Vaccination and Vector Control

2021 ◽  
Vol 9 (1) ◽  
pp. 198-212
Author(s):  
Cheryl Q. Mentuda
Keyword(s):  
Optimal Control ◽  
Vector Control ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Model Comparison ◽  
Reproduction Number ◽  
Control Strategies ◽  
Minimum Principle ◽  
Transmitted Disease ◽  
The Basic Reproduction Number

Abstract Dengue is the most common mosquito-borne viral infection transmitted disease. It is due to the four types of viruses (DENV-1, DENV-2, DENV-3, DENV-4), which transmit through the bite of infected Aedes aegypti and Aedes albopictus female mosquitoes during the daytime. The first globally commercialized vaccine is Dengvaxia, also known as the CYD-TDV vaccine, manufactured by Sanofi Pasteur. This paper presents a Ross-type epidemic model to describe the vaccine interaction between humans and mosquitoes using an entomological mosquito growth population and constant human population. After establishing the basic reproduction number ℛ0, we present three control strategies: vaccination, vector control, and the combination of vaccination and vector control. We use Pontryagin’s minimum principle to characterize optimal control and apply numerical simulations to determine which strategies best suit each compartment. Results show that vector control requires shorter time applications in minimizing mosquito populations. Whereas vaccinating the primary susceptible human population requires a shorter time compared to the secondary susceptible human.

scholarly journals State-Based Switching for Optimal Control of Computer Virus Propagation with External Device Blocking

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Qingyi Zhu ◽  
Seng W. Loke ◽  
Ye Zhang
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Minimum Principle ◽  
Optimal Solution ◽  
Computer Virus ◽  
Numerical Results ◽  
Difference Approximation ◽  
External Device ◽  
Virus Propagation ◽  
The Impact

The rapid propagation of computer virus is one of the greatest threats to current cybersecurity. This work deals with the optimal control problem of virus propagation among computers and external devices. To formulate this problem, two control strategies are introduced: (a) external device blocking, which means prohibiting a fraction of connections between external devices and computers, and (b) computer reconstruction, which includes updating or reinstalling of some infected computers. Then the combination of both the impact of infection and the cost of controls is minimized. In contrast with previous works, this paper takes into account a state-based cost weight index in the objection function instead of a fixed one. By using Pontryagin’s minimum principle and a modified forward-backward difference approximation algorithm, the optimal solution of the system is investigated and numerically solved. Then numerical results show the flexibility of proposed approach compared to the regular optimal control. More numerical results are also given to evaluate the performance of our approach with respect to various weight indexes.

scholarly journals Dynamic Analysis and Optimal Control of ISCR Rumor Propagation Model with Nonlinear Incidence and Time Delay on Complex Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Zhongxue Chang ◽  
Haijun Jiang ◽  
Shuzhen Yu ◽  
Shanshan Chen
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Complex Networks ◽  
Minimum Principle ◽  
Mean Field Theory ◽  
Mean Field ◽  
Propagation Model ◽  
Nonlinear Incidence ◽  
Rumor Propagation ◽  
Spreading Dynamics

An Innocents-Spreaders-Calmness-Removes (ISCR) rumor propagation model is established with nonlinear incidence and time delay on complex networks in this paper. Based on the mean-field theory, the spreading dynamics of the ISCR model are discussed in detail. Firstly, the basic reproduction number R 0 is obtained by the next generation matrix method to ensure the existence of rumor-prevailing equilibrium. Secondly, by utilizing the Routh–Hurwitz criterion and LaSalle’s invariance principle, the local stability and global stability of rumor equilibria are proved. Moreover, the optimal control is presented via Pontryagin’s minimum principle, which is to effectively restrain rumor diffusion. Finally, the theoretical results are verified by numerical simulations.

scholarly journals A Bio-Inspired Defensive Rumor Confinement Strategy in Online Social Networks

2021 ◽  
Vol 33 (1) ◽  
pp. 47-70
Author(s):  
Santhoshkumar Srinivasan ◽  
Dhinesh Babu L. D.
Keyword(s):  
Social Networks ◽  
Online Social Networks ◽  
Propagation Model ◽  
Information Propagation ◽  
Control Approach ◽  
Rumor Propagation ◽  
Immunization Strategies ◽  
New Information ◽  
The Individual ◽  
Rumor Control

Online social networks (OSNs) are used to connect people and propagate information around the globe. Along with information propagation, rumors also penetrate across the OSNs in a massive order. Controlling the rumor propagation is utmost important to reduce the damage it causes to society. Educating the individual participants of OSNs is one of the effective ways to control the rumor faster. To educate people in OSNs, this paper proposes a defensive rumor control approach that spreads anti-rumors by the inspiration from the immunization strategies of social insects. In this approach, a new information propagation model is defined to study the defensive nature of true information against rumors. Then, an anti-rumor propagation method with a set of influential spreaders is employed to defend against the rumor. The proposed approach is compared with the existing rumor containment approaches and the results indicate that the proposed approach works well in controlling the rumors.

scholarly journals Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Aristide G. Lambura ◽  
Gasper G. Mwanga ◽  
Livingstone Luboobi ◽  
Dmitry Kuznetsov
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Drug Administration ◽  
Mass Drug Administration ◽  
Helminth Infection ◽  
Reproduction Number ◽  
Control Strategies ◽  
Active Tuberculosis ◽  
Control Measures ◽  
The Impact

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

scholarly journals The Dynamics and Optimal Control of a Hand-Foot-Mouth Disease Model

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Hongwu Tan ◽  
Hui Cao
Keyword(s):  
Optimal Control ◽  
Reproduction Number ◽  
Control Strategies ◽  
Disease Model ◽  
Mouth Disease ◽  
Infected People ◽  
Hand Foot Mouth Disease ◽  
The Cost ◽  
Existence Of Equilibria ◽  
Disease Free

We build and study the transmission dynamics of a hand-foot-mouth disease model with vaccination. The reproduction number is given, the existence of equilibria is obtained, and the global stability of disease-free equilibrium is proved by constructing the Lyapunov function. We also apply optimal control theory to the hand-foot-mouth disease model. The treatment and vaccination interventions are considered in the hand-foot-mouth disease model, and the optimal control strategies based on minimizing the cost of intervention and minimizing the number of the infected people are given. Numerical results show the usefulness of the optimization strategies.

scholarly journals The Influence of User Protection Behaviors on the Control of Internet Worm Propagation

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yihong Li ◽  
Jinxiao Pan ◽  
Lipeng Song ◽  
Zhen Jin
Keyword(s):  
Reproduction Number ◽  
Control Strategies ◽  
Propagation Model ◽  
Sis Model ◽  
Worm Propagation ◽  
Internet Worm ◽  
User Behaviors ◽  
New Findings ◽  
And Control ◽  
User Protection

Computer users’ reactions to the outbreak of Internet worm directly determine the defense capability of the computer and play an important role in the spread of worm. In this paper, in order to characterize the impacts of adaptive user protection behaviors, an improved SIS model is proposed to describe the Internet worm propagation. The results of theoretical analysis indicate that the protective campaigns of users can indeed reduce the worm’s reproduction number to values less than one. But it may not be sufficient to eradicate the worm. In certain condition, a backward bifurcation leading to bistability can occur. These are new findings in the worm propagation model that bring new challenges to control the spread of the worm and further demonstrate the importance of user behaviors in controlling the worm propagation. Corresponding to the analysis results, defense and control strategies are provided.

scholarly journals Mathematical Modeling and Optimal Control Analysis of COVID-19 in Ethiopia

2020 ◽  
Author(s):  
Haileyesus Tessema Alemneh ◽  
Getachew Teshome Telahun
Keyword(s):  
Optimal Control ◽  
Necessary Conditions ◽  
Reproduction Number ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Control Model ◽  
Control Analysis ◽  
Basic Model ◽  
Short Period ◽  
Disease Free

In this paper we developed a deterministic mathematical model of the pandemic COVID-19 transmission in Ethiopia, which allows transmission by exposed humans. We proposed an SEIR model using system of ordinary differential equations. First the major qualitative analysis, like the disease free equilibruim point, endemic equilibruim point, basic reproduction number, stability analysis of equilibrium points and sensitivity analysis was rigorously analysed. Second, we introduced time dependent controls to the basic model and extended to an optimal control model of the disease. We then analysed using Pontryagins Maximum Principle to derive necessary conditions for the optimal control of the pandemic. The numerical simulation indicated that, an integrated strategy effective in controling the epidemic and the gvernment must apply all control strategies in combating COVID-19 at short period of time.

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