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Math. Biol."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    The aggregation and accumulation of oligomers of misfolded A\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\beta$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    -amyloids in the human brain is one of the possible causes for the onset of the Alzheimer\u2019s disease in the early stage. We introduce and study a new ODE model for the evolution of Alzheimer\u2019s disease based on the interaction between monomers, proto-oligomers, and oligomers of A\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\beta$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    amyloid protein in a small portion of the human brain, based upon biochemical processes such as polymerization, depolymerization, fragmentation and concatenation. We further introduce the possibility of controlling the evolution of the system via a treatment that targets the monomers and\/or the oligomers. We observe that a combined optimal treatment on both monomers and oligomers induces a substantial decrease of the oligomer concentration at the final stage. A single treatment on oligomers performs better than a single treatment on monomers. These results shed a light on the effectiveness of immunotherapy using anti-A\n                    <jats:inline-formula>\n                      <jats:tex-math>$$\\beta$$<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    antibodies, targeting monomers or oligomers. Several numerical simulations show how the oligomer concentration evolves without treatment, with single monomer\/oligomer treatment, or with a combined treatment.\n                  <\/jats:p>","DOI":"10.1007\/s00285-025-02256-3","type":"journal-article","created":{"date-parts":[[2025,8,8]],"date-time":"2025-08-08T12:03:08Z","timestamp":1754654588000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Optimal control of monomers and oligomers degradation in an Alzheimer\u2019s disease model"],"prefix":"10.1007","volume":"91","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9570-8532","authenticated-orcid":false,"given":"Iulia Martina","family":"Bulai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Ferraresso","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesca","family":"Gladiali","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,8,8]]},"reference":[{"key":"2256_CR1","doi-asserted-by":"publisher","first-page":"1369","DOI":"10.1007\/s00285-012-0591-0","volume":"67","author":"Y Achdou","year":"2013","unstructured":"Achdou Y, Franchi B, Marcello N, Tesi MC (2013) A qualitative model for aggregation and diffusion of $$\\beta$$-amyloid in Alzheimer\u2019s disease. 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