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However, misleading information on the effectiveness of vaccines has caused a decline in vaccination coverage in some countries, leading to the reappearance of related diseases. Therefore, a proper and well-planned pro-vax communication campaign may be effective in convincing people to get vaccinated. We formulate and solve a differential game with an infinite horizon played \u00e0 la Nash. The players involved in the game are the national healthcare system and a pharmaceutical firm that produces and sells a certain type of vaccine. The former aims to minimize the healthcare costs that unvaccinated people would entail. In turn, the pharmaceutical firm wants to minimize the missed profits from unsold vaccines. The two players run suitable vaccination advertising campaigns to diminish the <jats:italic>\u00e0-r\u00e9gime<\/jats:italic> number of unvaccinated. The Hamilton-Jacobi-Bellman approach is used to determine a Markovian-Nash equilibrium, studying how communication strategies can be effective in reducing the strength of anti-vax word of mouth.<\/jats:p>","DOI":"10.1007\/s10100-024-00917-0","type":"journal-article","created":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T05:01:53Z","timestamp":1715662913000},"page":"191-210","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Communication strategies to contrast anti-vax action: a differential game approach"],"prefix":"10.1007","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5238-8965","authenticated-orcid":false,"given":"Alessandra","family":"Buratto","sequence":"first","affiliation":[]},{"given":"Rudy","family":"Cesaretto","sequence":"additional","affiliation":[]},{"given":"Maddalena","family":"Muttoni","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,14]]},"reference":[{"issue":"1573","key":"917_CR1","doi-asserted-by":"publisher","first-page":"1669","DOI":"10.1098\/rspb.2005.3153","volume":"272","author":"C Bauch","year":"2005","unstructured":"Bauch C (2005) Imitation dynamics predict vaccinating behaviour. 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All authors have contributed to this paper, reviewed and approved the current form of the manuscript to be submitted. We confirm that all authors of the manuscript have no conflict of interest to declare.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}