{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:30:50Z","timestamp":1760243450491,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T00:00:00Z","timestamp":1666569600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The harvested logistic model with a slow variation in coefficients has been considered. Two cases, which depend on the harvest rate, were identified. The first one is when the harvest is subcritical, where the population evolves to an equilibrium. The other is supercritical harvesting, where the population decreases to zero at finite times. The single analytic approximate expression, which is capable of describing both harvesting cases, is readily and explicitly obtained using the multi-time scaling method together with the perturbation approach. This solution fits for a wide range of coefficient values. In addition, such an expression is validated by utilizing numerical computations, which are obtained by using the fourth-order Runge\u2013Kutta technique. Finally, the comparison shows a very good agreement between the two methods.<\/jats:p>","DOI":"10.3390\/axioms11110585","type":"journal-article","created":{"date-parts":[[2022,10,24]],"date-time":"2022-10-24T06:37:45Z","timestamp":1666593465000},"page":"585","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The General Analytic Expression of a Harvested Logistic Model with Slowly Varying Coefficients"],"prefix":"10.3390","volume":"11","author":[{"given":"Fahad M.","family":"Alharbi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Mecca 24382, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1126\/science.197.4302.463","article-title":"Harvesting natural populations in a randomly fluctuating environment","volume":"197","author":"Beddington","year":"1977","journal-title":"Science"},{"key":"ref_2","first-page":"171","article-title":"Fish harvesting management strategies using logistic growth model","volume":"41","author":"Laham","year":"2012","journal-title":"Sains Malays."},{"key":"ref_3","unstructured":"Banks, R.B. 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