Fractal and fractional SIS model for syphilis data

Area of Science:

• Epidemiology
• Mathematical Biology
• Dynamical Systems

Background:

• The Susceptible-Infectious-Susceptible (SIS) model is a fundamental tool in epidemiology.
• Fractional and fractal calculus offer advanced methods for modeling complex phenomena, including disease spread.
• Existing models may not fully capture the intricate dynamics of infectious diseases.

Purpose of the Study:

• To extend the SIS model using fractional and fractal derivatives.
• To compare the efficacy of standard, fractional, and fractal SIS models in describing real-world epidemic data.
• To investigate the impact of modified fractal orders on model performance.

Main Methods:

• Development of explicit and numerical solutions for standard, fractional, and fractal SIS models.
• Application and fitting of the models to Brazilian syphilis data (2011-2021).
• Calculation of the correlation coefficient (r) to assess model fit accuracy.
• Introduction of a modified fractal formulation with dual fractal orders and weights.

Main Results:

• The fractal SIS model demonstrated a better fit to syphilis data than standard or fractional models, indicated by a higher correlation coefficient.
• Estimated epidemiological parameters include an 11.6-day recovery period and a basic reproduction number (R0) of 6.5.
• A modified fractal formulation with two distinct fractal orders and weights further improved the model's descriptive accuracy.

Conclusions:

• Fractional and fractal derivatives provide valuable extensions to classical epidemic models.
• The fractal SIS model, particularly with modifications, offers a superior framework for analyzing and predicting infectious disease spread.
• This approach enhances our understanding of disease dynamics and improves data fitting for public health insights.