Dynamical analysis and optimal control of the developed information transmission model

PLOS ONE RESEARCH ARTICLE Dynamical analysis and optimal control of the developed information transmission model Sida Kang1, Xilin Hou ID1*, Yuhan Hu2, Hongyu Liu3 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 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Kang S, Hou X, Hu Y, Liu H (2022) Dynamical analysis and optimal control of the developed information transmission model. PLoS ONE 17(5): e0268326. https://doi.org/10.1371/ journal.pone.0268326 Editor: Mohammed S. Abdo, Hodeidah University, YEMEN Received: February 23, 2022 Accepted: April 26, 2022 Published: May 23, 2022 Peer Review History: PLOS recognizes the benefits of transparency in the peer review process; therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. The editorial history of this article is available here: https://doi.org/10.1371/journal.pone.0268326 Copyright: © 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. Data Availability Statement: All relevant data are within the paper. Funding: This article is supported by National Natural Science Foundation of China (NNSFC) grant 71472080, Humanities and Social Sciences * 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 S2EIR 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, R0. 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. 1 Introduction Information is a necessary component of human society’s development and has significant impacts on human life. In terms of the impact of information on human society, it can be broadly classified as either positive or negative. For instance, knowledge transmission [1, 2] and innovation capability transmission [3] are beneficial to social development, which constitutes positive information, whereas the spread of rumors [4, 5] and computer viruses [6–8] constitutes negative information. It can be classified into two broad categories of information transmission channels: contact transmission [9, 10] and network transmission [11, 12]. As a result, it is necessary to investigate the mechanisms of information transmission and control. PLOS ONE | https://doi.org/10.1371/journal.pone.0268326 May 23, 2022 1 / 23 PLOS ONE Research Projects of Education Department of Liaoning Province China grant 2020LNJC11 and LJKZ0311. Competing interests: The authors have declared that no competing interests exist. Dynamical analysis and optimal control of the developed information transmission model The information transmission characteristics are strikingly similar to those of infectious disease and rumor transmission [13, 14]. Thus, the information transmission models are frequently enhanced using infectious disease and rumor transmission models. The spread of infectious diseases was the first spreading problem studied by scholars. Infectious disease models that are frequently used include the SI model, the SIS model, and the SIR model [15–17]. Daley and Kendal developed a model of rumor transmission based on the classical infectious disease model. Scholars refer to this model as the DK model [18]. Based on the classical model of rumor transmission, scholars proposed the SEIR model with lurkers [19], the SIVR model with mutants [20], the SIVRS model with restorers [21], the SIHR model with forgetting and memory mechanisms [22], the SHIR model with hesitation mechanisms [23], and the SLIS model with age-structured [24]. In the last five years, scholars have conducted in-depth studies on information transmission from the following perspectives: (1) in terms of information type. Liu et al. developed a new SEIR model for heterogeneous networks to better understand the dynamics of information transmission in microblogs [25]. Wan et al. proposed the SIB model for analyzing the transmission of information about e-commerce discounts on a scale-free network [26]. Hosseini et al. developed the SEIRS-QV model with vaccination and isolation strategies to investigate malware transmission behavior in heterogeneous networks while also accounting for additional influencing factors such as user perception and network delay [27]. He et al. hypothesized that there is competition for various types of information in online social networks. They proposed the CISIR model to shed light on information competition and transmission [28]. Xiao et al. considered the dynamic changes in anti-rumor information from different aspects. They developed an evolutionary game theory-based driving mechanism for information, and ultimately proposed the SKIR model of rumor and anti-rumor competition [29]. (2) in terms of individual transmission, Zhang et al. examined the coexistence of rumors and authoritative information in social networks. They proposed the IS1 S2 C1 C2 R1 R2 model, which includes a super transmitter, a super authoritative information transmitter, a rumor suppressor, and a super authoritative information suppressor [30]. Li et al. believed that education had a significant impact on information transmission in a multi-language and heterogeneous network environment. As a result of this issue, the Ik S1k S2k R1k R2k model was proposed [12]. Sang et al. hypothesized (...truncated)