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In the case of multiple phases of infection, a generalized saturated incidence rate model is more reasonable than a simply saturated incidence because it captures the complex dynamics of the different infection phases. In contrast, a simple saturated incidence rate model assumes a fixed shape for the incidence rate curve, which may not accurately reflect the dynamics of multiple infection phases. Considering HBV and its various phases, we constructed a model to present the dynamics and control strategies using the generalized saturated incidence. First, we proved that the model is well-posed. We then found the reproduction quantity and model equilibria to discuss the time dynamics of the model and investigate the conditions for stabilities. We also examined a control mechanism by introducing various controls to the model with the aim to increase the population of those recovered and minimize the infected people. We performed numerical experiments to check the biological significance and control implementation.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/mbe.2024230","type":"journal-article","created":{"date-parts":[[2024,3,6]],"date-time":"2024-03-06T10:26:20Z","timestamp":1709720780000},"page":"5207-5226","source":"Crossref","is-referenced-by-count":6,"title":["Modeling different infectious phases of hepatitis B with generalized saturated incidence: An analysis and control"],"prefix":"10.3934","volume":"21","author":[{"given":"Tahir","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, UAE University, P.O.Box 15551, Al-Ain, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fathalla A.","family":"Rihan","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, UAE University, P.O.Box 15551, Al-Ain, United Arab Emirates"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad","family":"Ibrahim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Malakand Chakdara, Dir (L), Pakhtunkhwa, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Data Sciences, Changji University, Changji 831100, Xinjiang, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Atif M.","family":"Alamri","sequence":"additional","affiliation":[{"name":"Software Engineering Department, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Salman A.","family":"AlQahtani","sequence":"additional","affiliation":[{"name":"Computer Engineering Department, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2024230-1","doi-asserted-by":"publisher","unstructured":"M. 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