Fractal and fractional SIS model for syphilis data

Author:

Gabrick Enrique C.1ORCID,Sayari Elaheh1ORCID,Souza Diogo L. M.1ORCID,Borges Fernando S.2ORCID,Trobia José3ORCID,Lenzi Ervin K.14ORCID,Batista Antonio M.13ORCID

Affiliation:

1. Graduate Program in Science, State University of Ponta Grossa 1 , 84030-900 Ponta Grossa, PR, Brazil

2. Department of Physiology and Pharmacology, State University of New York Downstate Health Sciences University 2 , Brooklyn, New York 11203, USA

3. Center for Mathematics, Computation, and Cognition, Federal University of ABC, 09606-045 São Bernardo do Campo, SP 3 , Brazil

4. Department of Physics, State University of Ponta Grossa 4 , 84030-900 Ponta Grossa, PR, Brazil

Abstract

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.

Funder

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Fundação de Amparo à Pesquisa do Estado de São Paulo

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Publisher

AIP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

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