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Recent advances in the development of complement-specific drugs in several rare diseases have opened the gateways to apply complement interventions toward a broader array of pathologies. However, this goal remains elusive due to the complexity and the multifaceted roles of the complement system. Mechanistic mathematical models can provide an effective tool to integrate the different mechanisms, features, and feedback loops into a framework that allows the simulation of complement dynamics under different conditions and the prediction of the effect of interventions. In this scoping review, we provide an overview of current mathematical models of the complement system, open problems related to complement biology, and discuss future work on how mechanistic mathematical modeling of the complement system can potentially alleviate some of the challenges in complement biology.<\/jats:p>","DOI":"10.1007\/s11538-026-01723-2","type":"journal-article","created":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T12:45:46Z","timestamp":1790858746000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mathematical Modeling of the Complement System: a Scoping Review"],"prefix":"10.1007","volume":"88","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3608-9356","authenticated-orcid":false,"given":"Luis","family":"Sordo Vieira","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5832-5228","authenticated-orcid":false,"given":"Daniel","family":"Cruz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1052-8306","authenticated-orcid":false,"given":"Ivan","family":"Ramirez-Zuniga","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0067-0210","authenticated-orcid":false,"given":"Carl","family":"Atkinson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5198-065X","authenticated-orcid":false,"given":"Borna","family":"Mehrad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9143-9451","authenticated-orcid":false,"given":"Reinhard","family":"Laubenbacher","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,10,1]]},"reference":[{"issue":"2","key":"1723_CR1","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1038\/s41577-021-00665-1","volume":"22","author":"B Afzali","year":"2022","unstructured":"Afzali B, Noris M, Lambrecht BN, Kemper C (2022) The state of complement in COVID-19. 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