2023/09/12 by Enrique C. Gabrick, Elaheh Sayari, Gabrick, Enrique C. +11 · 1 citation
Medicine · #Biological Physics (physics.bio-ph) #Data-Driven Disease Surveillance #FOS: Physical sciences #Physics and Society (physics.soc-ph)
paper · pdf · doi:10.48550/arxiv.2309.06209
openalex publication_date 2023/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This work studies the SIS model extended by fractional and fractal derivatives. 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.