Caputo SIR model for COVID-19 under optimized fractional order

Area of Science:

• Epidemiology
• Mathematical Modeling
• Fractional Calculus

Background:

• The global spread of coronavirus has caused significant disruption and mortality.
• Sophisticated epidemiological models are being developed, but simpler approaches may offer valuable insights.

Purpose of the Study:

• To evaluate the efficacy of a Susceptible-Infectious-Recovered (SIR) epidemiological model incorporating a Caputo derivative for analyzing COVID-19 data in Pakistan.
• To compare the fitting accuracy of the Caputo SIR model against the classical SIR model using real-world case data.

Main Methods:

• Application of a SIR model with a Caputo fractional derivative to epidemic data from Pakistan (April 1 - March 15, 2020).
• Analysis of qualitative behavior using the Banach contraction principle for uniqueness.
• Stability analysis and investigation of the basic reproduction number using Ulam-Hyers stability.
• Parameter estimation via nonlinear least-squares curve fitting.

Main Results:

• The Caputo SIR model provided a superior fit to the infectious compartment data compared to the classical SIR model.
• An average absolute relative error reduction of approximately 48% was observed with the Caputo operator.
• Time series and 3D contour plots indicated that social distancing is the most effective strategy for epidemic control.

Conclusions:

• The Caputo SIR model offers improved accuracy for fitting real-world epidemic data.
• Mathematical modeling with fractional calculus can enhance epidemiological analysis.
• Social distancing remains a critical public health intervention for managing infectious disease outbreaks.