Optimal control of a rumor propagation model with latent period in emergency event

Huo, Liang’an; Lin, Tingting; Fan, Chao; Liu, Chen; Zhao, Jun

doi:10.1186/s13662-015-0394-x

Cited by 39 publications

(19 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Stochastic control is a potential candidate for resolving this issue. This concept has widely been applied to optimization of dynamical systems driven by stochastic fluctuations arising in finance, economics, insurance, and social science . A powerful tactic for solving a stochastic control problem, especially that based on a system of SDEs, is finding an appropriate solution to a Hamilton‐Jacobi‐Bellman (HJB) equation, which is a degenerate parabolic partial differential equation to determine the optimal control of the system.…”

Section: Introductionmentioning

confidence: 99%

Modeling stochastic operation of reservoir under ambiguity with an emphasis on river management

Yoshioka

2019

Optim Control Appl Methods

View full text Add to dashboard Cite

An optimization problem of controlling a dam installed in a river is analyzed based on a stochastic control formalism of a diffusion process under model ambiguity: a new mathematical approach to this issue. The diffusion process is a pathwise unique solution to a water balance equation considering the inflow, outflow, water loss in the reservoir, and direct rainfall. Finding the optimal reservoir operation policy reduces to solving a degenerate parabolic partial differential equation: a Hamilton-Jacobi-Bellman-Isaacs equation. A monotone finite difference scheme is constructed for discretization of the equation, successfully generating nonoscillatory and reasonably accurate numerical solutions. Stability analysis of the resulting water balance dynamics is finally carried out for both environmentally friendly and not friendly reservoir operations. KEYWORDS finite difference scheme, Hamilton-Jacobi-Bellman-Isaacs equation, reservoir operation, stochastic control, viscosity solution INTRODUCTIONThis paper contributes to providing a mathematical framework for modeling and control of reservoirs created in rivers.Since the problem has an engineering background, it is first presented, and then, the issues to be addressed and our contributions are explained.Many rivers have dams serving as central infrastructures to supply essential water resources for human lives. 1-3 The stored water in the reservoir created by a dam is utilized for multiple purposes, such as drinking water, irrigation, and hydropower generation. 4 Several dams are used for flood mitigation as well. 5,6 On the other hand, controlling a dam critically affects its downstream river environment because the original flow regime is altered. 7-9 Sediment transport and attached algae population dynamics in dam downstream experience significant changes because dams trap sediment and the algae growth is highly flow-dependent. 10 Dam operation is thus desired to be environmentally friendly such that its impacts on the downstream are minimized, while it should be fit-for-purpose at the same time.Management of environment and ecology in rivers has been a long-standing engineering problem, 11-13 and mathematical tools and concepts for their modeling, analysis, and control are still developing. Several researchers considered river management problems based on stochastic process models such as stochastic differential equations (SDEs) 14 that can naturally consider stochasticity involved in environmental and ecological processes. 15 Interactions between aquatic species, such as riparian vegetation and fishes, and river discharges have been described with SDEs. 16 Miyamoto and Kimura 17 analyzed seedling, growth, and mortality dynamics of riparian trees subject to stochastic flood disturbances. Vesipa et al 18 764

show abstract

Section: Introductionmentioning

confidence: 99%

Modeling stochastic operation of reservoir under ambiguity with an emphasis on river management

Yoshioka

2019

Optim Control Appl Methods

View full text Add to dashboard Cite

show abstract

“…[10] for a popular introduction of the model. Since then, a multitude of rumor spreading models based on homogeneous networks have been proposed [11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

An effective rumor-containing strategy

Pan

Yang

et al. 2018

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

False rumors can lead to huge economic losses or/and social instability. Hence, mitigating the impact of bogus rumors is of primary importance. This paper focuses on the problem of how to suppress a false rumor by use of the truth. Based on a set of rational hypotheses and a novel rumor-truth mixed spreading model, the effectiveness and cost of a rumor-containing strategy are quantified, respectively. On this basis, the original problem is modeled as a constrained optimization problem (the RC model), in which the independent variable and the objective function represent a rumor-containing strategy and the effectiveness of a rumor-containing strategy, respectively. The goal of the optimization problem is to find the most effective rumor-containing strategy subject to a limited rumor-containing budget. Some optimal rumor-containing strategies are given by solving their respective RC models. The influence of different factors on the highest cost effectiveness of a RC model is illuminated through computer experiments. The results obtained are instructive to develop effective rumor-containing strategies. equation. Due to the exact modeling and the perfect accommodation of the network topology, this model characterizes the SIS epidemics more accurately as compared with all previous SIS models. Moreover, this model is analytically tractable, resulting in profound conclusions. In recent years, this individual-based modeling approach has been widely applied to areas such as epidemic spreading [42][43][44], malware propagation [45][46][47][48][49][50][51][52], cyber security [53][54][55][56][57], and message transmission [58]. To our knowledge, to date the rumor-containing problem has not yet been studied under individual-level rumor spreading models.Clarifying rumors by releasing truths is a common way to inhibit rumors [59,60]. In this context, every individual may choose to believe the rumor or believe the truth or be uncertain. This paper focuses on the problem of how to inhibit a false rumor by use of the truth. Based on a novel individual-level rumor-truth mixed spreading model, the effectiveness and cost of a rumor-containing strategy are quantified. Thereby, the original problem is modeled as a constrained optimization problem (the rumor-containing (RC) model), in which the independent variable and the objective function represent a rumor-containing strategy and the effectiveness of a rumor-containing strategy, respectively. The goal of the optimization problem is to find the most effective rumor-containing strategy subject to a limited rumor-containing budget. Some optimal rumor-containing strategies are given by solving their respective RC models. The influence of different factors on the highest cost effectiveness of a RC model is uncovered through computer simulations. These results are condusive to the design of practical rumor-containing strategies. To our knowledge, this is the first time the rumor-containing problem is treated in this way.The subsequent materials of this work are organized in this fashion: ...

show abstract

“…From the perspective of economy, optimal control is used to seek a reasonable tradeoff between cost and benefit. In this context, it has been widely used in the control application of 2 Security and Communication Networks biological viruses [15][16][17][18][19], rumors [20,21], and others [22,23]. Inspired by these, Zhu et al proposed a delayed SIR model for computer virus propagation [24].…”

Section: Introductionmentioning

confidence: 99%

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

Zhu

Loke

Zhang

2018

Security and Communication Networks

View full text Add to dashboard Cite

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.

show abstract

Optimal control of a rumor propagation model with latent period in emergency event

Cited by 39 publications

References 22 publications

Modeling stochastic operation of reservoir under ambiguity with an emphasis on river management

Modeling stochastic operation of reservoir under ambiguity with an emphasis on river management

An effective rumor-containing strategy

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

Contact Info

Product

Resources

About