ApproximantCoefficientsSIR

ApproximantCoefficientsSIR computes approximate analytic solutions for the SIR (Susceptible-Infectious-Recovered) epidemic model by deriving coefficients of Asymptotic Approximants to regularize divergent power series and produce closed-form approximations, and is implemented in MATLAB.

Key Features:

• Analytical Continuation: Employs analytical continuation of divergent power series to align solutions with the long-term asymptotic behavior of the SIR model.
• Asymptotic Approximant Construction: Uses Asymptotic Approximants to construct convergent series representations that yield closed-form approximations for SIR variables.
• Coefficient Calculation: Computes the coefficients of the Asymptotic Approximant that define the analytic approximation.
• MATLAB Implementation: Implemented in MATLAB to perform the required symbolic and numeric computations.

Scientific Applications:

• Epidemiological Modeling: Provides analytic solutions to analyze dynamics of infectious disease spread within the SIR framework.
• Pandemic Analysis: Applicable to modeling real-world epidemic curves such as COVID-19 to examine infection rates, peak timing, and recovery patterns.
• Predictive Modeling: Supports development of predictive approximations for outbreak trajectories using closed-form representations.
• Parameter Sensitivity Analysis: Enables assessment of how variations in SIR model parameters affect disease dynamics via the approximant coefficients.
• Educational Use: Serves as an example for applying asymptotic methods and analytic continuation in mathematical epidemiology.

Methodology:

Asymptotic analysis of the SIR model to identify long-term behavior and key parameters.
Construction of Asymptotic Approximants to bridge divergent power series and target analytic forms.
Computation of the coefficients of the Asymptotic Approximant that specify the closed-form approximation.