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Considering the interaction and coexistence of both positive and negative public opinion information (referred to as public opinion), it is of great significance for social development and economic stability to understand the co-evolution process of competitive public opinion and compress the spreading space of negative public opinion. Allowing for this point, this paper constructed a two-stage spreading model of competitive public opinion combing with the actual case of public opinion propagation, analysed the main factors influencing the co-evolution process, such as netizens\u2019 intimacy, network literacy, and so on, and redefined netizens\u2019 state transition probability matrix with the help of Markov process. Then, the effectiveness of the spreading model was verified and the propagation rule of public opinion was discussed in open and closed OSN through simulation experiments. Finally, the intervention strategies were proposed and optimised with the limitation of cost. The results show that the propagation of public opinion mainly depends on netizens\u2019 behaviour with low literacy and presents difference characteristics in two types of OSN. During the intervention process of public opinion propagation, there exists an effective intervention interval and the best intervention strategy varies with the change of network topology. Our research provided a cornerstone for further understanding of the co-evolution process of competitive public opinion and the research conclusions also provided a certain decision-making reference for enterprises, governments and other regulators to reasonably respond to the propagation of public opinion.<\/jats:p>","DOI":"10.1177\/01655515221141033","type":"journal-article","created":{"date-parts":[[2023,1,2]],"date-time":"2023-01-02T04:36:01Z","timestamp":1672634161000},"page":"463-480","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["Research on the co-evolution of competitive public opinion and intervention strategy based on Markov process"],"prefix":"10.1177","volume":"51","author":[{"given":"Xiaolei","family":"Liu","sequence":"first","affiliation":[{"name":"School of Economics and Management, Harbin Engineering University, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6091-9997","authenticated-orcid":false,"given":"Jiakun","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Economics and Management, Shandong University of Science and Technology, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yun","family":"Li","sequence":"additional","affiliation":[{"name":"College of Economics and Management, Shandong University of Science and Technology, China; College of Foreign Languages, Shandong University of Science and Technology, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2023,1,2]]},"reference":[{"key":"e_1_3_3_2_2","unstructured":"Simon K. 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