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We obtain explicit solutions for the standard and fractal formulations; for the fractional case, we study numerical solutions. As a real data example, we consider the Brazilian syphilis data from 2011 to 2021. We fit the data by considering the three variations of the model. Our fit suggests a recovery period of 11.6 days and a reproduction ratio (R0) equal to 6.5. By calculating the correlation coefficient (r) between the real data and the theoretical points, our results suggest that the fractal model presents a higher r compared to the standard or fractional case. The fractal formulation is improved when two different fractal orders with distinguishing weights are considered. This modification in the model provides a better description of the data and improves the correlation coefficient.<\/jats:p>","DOI":"10.1063\/5.0153122","type":"journal-article","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T13:42:20Z","timestamp":1694785340000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":12,"title":["Fractal and fractional SIS model for syphilis data"],"prefix":"10.1063","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8407-7675","authenticated-orcid":false,"given":"Enrique C.","family":"Gabrick","sequence":"first","affiliation":[{"name":"Graduate Program in Science, State University of Ponta Grossa 1 , 84030-900 Ponta Grossa, PR, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6183-9393","authenticated-orcid":false,"given":"Elaheh","family":"Sayari","sequence":"additional","affiliation":[{"name":"Graduate Program in Science, State University of Ponta Grossa 1 , 84030-900 Ponta Grossa, PR, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-0007-1238","authenticated-orcid":false,"given":"Diogo L. 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