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In the Poissonian case, we obtain totally explicit results, prove that the mean care time converges to a constant and give numerical examples. We also propose an analysis of the impact of working conditions on the average time that can be devoted to a patient. Four scenarios are proposed with numerical applications. Our analysis provides insights into current discussions on the introduction of caregiver ratios in hospitals to improve both the quality of care and caregivers\u2019 working conditions. <\/jats:p>","DOI":"10.1142\/s0219198924400048","type":"journal-article","created":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T07:54:56Z","timestamp":1714118096000},"source":"Crossref","is-referenced-by-count":0,"title":["Assessing Available Care Time and Nursing Shortage in a Hospital"],"prefix":"10.1142","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9560-4074","authenticated-orcid":false,"given":"Romain","family":"Biard","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Franche Comt\u00e9, CNRS, LmB (UMR 6623), F-25000 Besan\u00e7on, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6187-2924","authenticated-orcid":false,"given":"Marc","family":"Deschamps","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Franche-Comt\u00e9, CRESE, F-25000 Besan\u00e7on, France"},{"name":"OFCE, Sciences Po, Place de Catalogne 75014, Paris, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2070-5801","authenticated-orcid":false,"given":"Mostapha","family":"Diss","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Franche-Comt\u00e9, CRESE, F-25000 Besan\u00e7on, France"},{"name":"Africa Institute for Research in Economics and Social Sciences (AIRESS), University Mohammed VI Polytechnic, Rabat, Morocco"}]},{"given":"Alexis","family":"Roussel","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Franche-Comt\u00e9, CRESE, F-25000 Besan\u00e7on, France"}]}],"member":"219","published-online":{"date-parts":[[2024,5,20]]},"reference":[{"key":"S0219198924400048BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s13235-016-0197-z"},{"key":"S0219198924400048BIB002","first-page":"127","volume-title":"Cournot, \u00c9conomie et Philosophie","author":"Bernhard P.","year":"2020"},{"key":"S0219198924400048BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s13235-020-00354-z"},{"key":"S0219198924400048BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2016.01.004"},{"key":"S0219198924400048BIB005","first-page":"43","volume":"176","author":"Biard R.","year":"2021","journal-title":"Rev. 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