{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T23:41:41Z","timestamp":1791416501514,"version":"4.3.3"},"reference-count":48,"publisher":"Wiley","issue":"10","license":[{"start":{"date-parts":[[2013,10,1]],"date-time":"2013-10-01T00:00:00Z","timestamp":1380585600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Periodontology"],"published-print":{"date-parts":[[2013,10]]},"abstract":"<jats:p><jats:bold>Background:<\/jats:bold> This study aims to expand on a previously presented cellular automata model and further explore the non\u2010linear dynamics of periodontitis. Additionally the authors investigated whether their mathematical model could predict the two known types of periodontitis, aggressive (AgP) and chronic periodontitis (CP).<\/jats:p><jats:p><jats:bold>Methods:<\/jats:bold> The time evolution of periodontitis was modeled by an iterative function, based on the hypothesis that the host immune response level determines the rate of periodontitis progression. The chaotic properties of this function were investigated by direct iteration, and the model was validated by immunologic and clinical parameters derived from two clinical study populations.<\/jats:p><jats:p><jats:bold>Results:<\/jats:bold> Periodontitis can be described as chaos with the level of the host immune response determining its progression rate; the dynamics of the proposed model suggest that by increasing the host immune response level, periodontitis progression rate decreases. Renormalization transformations show the presence of two overlapping zones of disease activity corresponding to AgP and CP. By <jats:italic>k<\/jats:italic>\u2010means cluster analysis, immunologic parameters corroborated the findings of the renormalization transformations. Periodontitis progression rates are modeled to scale with a power law of 1.3, and the mean exponential speed of the system is found to be 1.85 (metric entropy); clinical datasets confirmed the mathematical estimates.<\/jats:p><jats:p><jats:bold>Conclusions:<\/jats:bold> This study introduces a mathematical model that identifies periodontitis as a non\u2010linear chaotic process. It offers a quantitative assessment of the disease progression rate and identifies two zones of disease activity that correspond to the existing classification of periodontitis in the AgP and CP types.<\/jats:p>","DOI":"10.1902\/jop.2013.120637","type":"journal-article","created":{"date-parts":[[2013,3,28]],"date-time":"2013-03-28T11:13:13Z","timestamp":1364469193000},"source":"Crossref","is-referenced-by-count":17,"title":["Mathematical Modeling Suggests That Periodontitis Behaves as a Non\u2010Linear Chaotic Dynamical Process"],"prefix":"10.1002","volume":"84","author":[{"given":"G.","family":"Papantonopoulos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"K.","family":"Takahashi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"T.","family":"Bountis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"B.G.","family":"Loos","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2013,10]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1600-0757.2011.00415.x"},{"key":"e_1_2_7_3_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1600-0757.2005.00107.x"},{"key":"e_1_2_7_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1600-0757.2006.00187.x"},{"key":"e_1_2_7_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1600-0757.2006.00188.x"},{"key":"e_1_2_7_6_1","doi-asserted-by":"publisher","DOI":"10.1902\/annals.1999.4.1.1"},{"key":"e_1_2_7_7_1","unstructured":"KaplanD GlassL.Understanding Nonlinear Dynamics. 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