A rumor transmission model with various contact interactions

Kawachi, Kazuki; Seki, M.; Yoshida, Hayato; Otake, Yohei; Warashina, Katsuhide; Ueda, Hiroshi

doi:10.1016/j.jtbi.2007.11.024

Cited by 80 publications

(53 citation statements)

References 13 publications

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“…By using basic reproduction number 0 , he investigated sufficient conditions for the local stability of equilibrium point and for the uniform strong persistence [5]. For examining what influences the spread of rumor from various angles, Kawachi et al [6] suggested a rumor transmission model with various contact interactions. Huo et al [7] analyzed the rumor model with incubation by 2 Discrete Dynamics in Nature and Society using 0 .…”

Section: Introductionmentioning

confidence: 99%

Optimal Control Strategies Depending on Interest Level for the Spread of Rumor

Jeong

Kim

Jung

2018

Discrete Dynamics in Nature and Society

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Many media channels such as broadcast, newspaper, and social networks diffuse a variety of information which can cause spread of many rumors. There are social damage and economic damage due to the spread of rumors. Thus one needs to establish strategies for controlling the rumors. We first propose rumor model with three control strategies for preventing the spread of rumor, (1) announcing the truth before ignorant receives rumor, (2) punishing spreaders, and (3) deleting information of the rumor in media, and consider optimal control problems to minimize the number of spreaders while minimizing the cost of three control strategies for preventing the spread of rumors. The analysis of optimal control problems is conducted as Pontryagin's Maximum Principle. Furthermore, adapted optimal control is performed to investigate the effect of three controls under isoperimetric constraints. By using numerical simulations, we compare the number of spreaders before and after applying the three controls and confirm when and how each control should be applied with respect to the interest level of rumor. The lower the interest level of rumor is, the greater the number of spreaders drops after the three controls are applied. In terms of timing of three controls, control (1) should be applied in the early stage of rumor spreading and control (2) is required when the rumors spread the most. After the rumors spread the most, control (3) is needed. Commonly the higher the interest level is, the more controls (1) and (2) are required. On the other hand, control (3) is needed a lot when the interest level is low.

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Section: Introductionmentioning

confidence: 99%

Optimal Control Strategies Depending on Interest Level for the Spread of Rumor

Jeong

Kim

Jung

2018

Discrete Dynamics in Nature and Society

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“…Many mathematical models have been introduced to study the dynamics of human behavior in response to the spread of rumors, such as in [2,3,4,5,6,7,8,9]. In this article, we develop a model based on a previous model introduced by the authors in [1].…”

Section: Introductionmentioning

confidence: 99%

An Analysis of Rumor Spreading Model With Contra Productive Intervention

Aldila¹,

Paramartha²,

Tasman³

2017

Int. J. of Pure and Appl. Math.

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Abstract:A mathematical model to explain the spread of rumors in a closed human population is proposed in this article. Interventions from the government to educate people about the danger of rumor along with apprehensions of fanatical people are implemented in the model. Intervention of imprisonment which will send fanatical people to prison was assumed to have a worsening effect, i.e increasing the ability of fanatical people to persuade other people to follow their ideology. Equilibrium points and their local stability criteria are discussed. Some scenarios that might appear in reality have been shown numerically to give a better illustration of the model.

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“…If the campaigns were effective, the growth rate will high. There were many growth model studies regarding rumors (Huo et al, 2012, Kawachi, 2006, 2008a, 2008bKawachi et al, 2008). The growth model study of rumors stemmed from a mathematical epidemic model (Kermack and McKendrick, 1991;Murray, 1989).…”

Section: Introductionmentioning

confidence: 99%

A Study of Sales Increase and/or Decrease by Campaign Using a Differential Equation Model of the Growth Phenomenon

Horinouchi¹,

Takabayashi²,

Yamamoto³

et al. 2014

Industrial Engineering and Management Systems

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With society becoming more advanced and complex, the required management engineering makes essential the development of human resources that can propose solutions for problems of new phenomena from a different perspective. As an example of such phenomena, we note a consumer electronics 'Eco-point' system campaign in this study. To mitigate global warming, revitalize the economy, and encourage the adoption of terrestrial digital compatible TVs, the consumer electronics Eco-point system campaign was implemented in May 2009 in Japan. In this study, we note a model which is constant term with exponential curve with notion of the growth phenomenon (Nakagiri and Kurita, Journal of the Operations Research Society of Japan, 2002). In our study, we call this model the 'differential equation model of the growth phenomenon.' This model represents a phenomenon with a hierarchical structure for capturing the properties of n species. In this study, we propose a new model which can represent not only the impact of largescale campaigns but also seasonal factors. Accordingly, we understand the phenomenon of fluctuation of sales of some products caused by large-scale campaigns and predict the fluctuation of sales. The final goal of this study is to develop human resources that can propose provision and solution for pre-consumption and reactionary decline in demand by understanding the impact of large-scale campaigns. As the first step of this goal, our objective is to propose a new regression method with different conventional perspective that can describe the fluctuation of sales caused by large-scale campaigns and show the possibility of new management engineering education.

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A rumor transmission model with various contact interactions

Cited by 80 publications

References 13 publications

Optimal Control Strategies Depending on Interest Level for the Spread of Rumor

Optimal Control Strategies Depending on Interest Level for the Spread of Rumor

An Analysis of Rumor Spreading Model With Contra Productive Intervention

A Study of Sales Increase and/or Decrease by Campaign Using a Differential Equation Model of the Growth Phenomenon

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