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      Dynamical analysis and optimal control of the developed information transmission model

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      PLoS ONE
      Public Library of Science

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          Abstract

          Information transmission significantly impacts social stability and technological advancement. This paper compares the phenomenon of “Super transmission” and “Asymptomatic infection” in COVID-19 transmission to information transmission. The former is similar to authoritative information transmission individuals, whereas the latter is similar to individuals with low acceptance in information transmission. It then constructs an S2 EIR model with transmitter authority and individual acceptance levels. Then, it analyzes the asymptotic stability of information-free and information-existence equilibrium on a local and global scale, as well as the model’s basic reproduction number, R 0. Distinguished with traditional studies, the population density function and Hamiltonian function are constructed by taking proportion of “Super transmitter” and proportion of hesitant group turning into transmitters as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively facilitate information transmission. The numerical simulation corroborates the theoretical analysis results and the system’s sensitivity to control parameter changes. The research results indicate that the authoritative “Super transmitter” has a beneficial effect on information transmission. In contrast, the “Asymptomatic infected individual” with poor individual acceptance level negatively affects information transmission.

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          Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.

          A precise definition of the basic reproduction number, R0, is presented for a general compartmental disease transmission model based on a system of ordinary differential equations. It is shown that, if R0 1, then it is unstable. Thus, R0 is a threshold parameter for the model. An analysis of the local centre manifold yields a simple criterion for the existence and stability of super- and sub-threshold endemic equilibria for R0 near one. This criterion, together with the definition of R0, is illustrated by treatment, multigroup, staged progression, multistrain and vector-host models and can be applied to more complex models. The results are significant for disease control.
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            Quantifying Trading Behavior in Financial Markets Using Google Trends

            Crises in financial markets affect humans worldwide. Detailed market data on trading decisions reflect some of the complex human behavior that has led to these crises. We suggest that massive new data sources resulting from human interaction with the Internet may offer a new perspective on the behavior of market participants in periods of large market movements. By analyzing changes in Google query volumes for search terms related to finance, we find patterns that may be interpreted as “early warning signs” of stock market moves. Our results illustrate the potential that combining extensive behavioral data sets offers for a better understanding of collective human behavior.
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              EPIDEMICS AND RUMOURS.

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                Author and article information

                Contributors
                Role: ConceptualizationRole: Data curationRole: Formal analysisRole: InvestigationRole: MethodologyRole: SoftwareRole: ValidationRole: Writing – original draft
                Role: ConceptualizationRole: Writing – review & editing
                Role: Data curationRole: Formal analysisRole: InvestigationRole: MethodologyRole: SoftwareRole: Validation
                Role: Writing – review & editing
                Role: Editor
                Journal
                PLoS One
                PLoS One
                plos
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                2022
                23 May 2022
                : 17
                : 5
                : e0268326
                Affiliations
                [1 ] Department of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan, Liaoning, China
                [2 ] Department of Science, University of Science and Technology Liaoning, Anshan, Liaoning, China
                [3 ] Department of Business Administration, University of Science and Technology Liaoning, Anshan, Liaoning, China
                Hodeidah University, YEMEN
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Author information
                https://orcid.org/0000-0002-9980-2876
                Article
                PONE-D-22-05396
                10.1371/journal.pone.0268326
                9132490
                35604920
                672a630a-e66a-45a4-85d1-041ef0f01e76
                © 2022 Kang et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 23 February 2022
                : 26 April 2022
                Page count
                Figures: 7, Tables: 1, Pages: 23
                Funding
                Funded by: funder-id http://dx.doi.org/10.13039/501100001809, National Natural Science Foundation of China;
                Award ID: 71472080
                Award Recipient :
                Funded by: Humanities and Social Sciences Research Projects of Education Department of Liaoning Province China
                Award ID: 2020LNJC11
                Award Recipient :
                Funded by: Humanities and Social Sciences Research Projects of Education Department of Liaoning Province China
                Award ID: LJKZ0311
                Award Recipient :
                This article is supported by National Natural Science Foundation of China (NNSFC) grant 71472080, Humanities and Social Sciences Research Projects of Education Department of Liaoning Province China grant 2020LNJC11 and LJKZ0311.
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