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dynamics on networks and interactions between networks; and dynamics developed over a network. As a typical application of complex networks, the dynamics of disease spreading and control strategies on networks have attracted widespread attention from researchers. We investigate the dynamics and optimal control for an epidemic model with demographics and heterogeneous asymmetric control strategies (immunization and quarantine) on complex networks. We derive the epidemic threshold and study the global stability of disease-free and endemic equilibria based on different methods. The results show that the disease-free equilibrium cannot undergo a Hopf bifurcation. We further study the optimal control strategy for the complex system and obtain its existence and uniqueness. Numerical simulations are conducted on scale-free networks to validate and supplement the theoretical results. The numerical results indicate that the asymmetric control strategies regarding time and degree of node for populations are superior to symmetric control strategies when considering control cost and the effectiveness of controlling infectious diseases. Meanwhile, the advantages of the optimal control strategy through comparisons with various baseline immunization and quarantine schemes are also shown.<\/jats:p>","DOI":"10.3390\/sym16020166","type":"journal-article","created":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T08:44:06Z","timestamp":1706690646000},"page":"166","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Propagation Dynamics of an Epidemic Model with Heterogeneous Control Strategies on Complex Networks"],"prefix":"10.3390","volume":"16","author":[{"given":"Yan","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Computer Science, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shanshan","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dingguo","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Media Engineering, Communication University of Zhejiang, Hangzhou 310018, China"},{"name":"Key Lab of Film and TV Media Technology of Zhejiang Province, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lixiang","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Shanghai University of Engineering Science, Shanghai 201620, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7454-4276","authenticated-orcid":false,"given":"Ke-Ke","family":"Shang","sequence":"additional","affiliation":[{"name":"Computational Communication Collaboratory, Nanjing University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20220051","DOI":"10.1360\/nso\/20220051","article-title":"Information overload: How hot topics distract from news\u2014COVID-19 spread in the US","volume":"2","author":"Yang","year":"2023","journal-title":"Natl. 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