Accurate closed-form solution of the SIR epidemic model

Area of Science:

• Mathematical modeling
• Epidemiology
• Computational mathematics

Background:

• The SIR (Susceptible-Infectious-Recovered) model is a fundamental tool in epidemiology for understanding disease spread.
• Traditional SIR model solutions often rely on numerical approximations, limiting analytical insights into long-term dynamics.
• Divergent power series solutions exist but require techniques to extract meaningful behavior.

Purpose of the Study:

• To derive an accurate closed-form solution for the SIR Epidemic Model.
• To develop a method for analytically continuing divergent power series solutions.
• To demonstrate the practical utility of the derived solution for real-world epidemic analysis, such as COVID-19.

Main Methods:

• Utilized Asymptotic Approximants to analytically continue a divergent power series solution of the SIR model.
• Matched the analytically continued series to the known long-time asymptotic behavior of the epidemic model.
• Applied the resulting closed-form solution to analyze the dynamics of the COVID-19 pandemic.

Main Results:

• An accurate closed-form solution for the SIR Epidemic Model was successfully obtained.
• The method effectively transforms a divergent series into a solution that accurately reflects long-term epidemic behavior.
• The analytical solution demonstrated utility in modeling aspects of the COVID-19 pandemic.

Conclusions:

• The Asymptotic Approximants method provides a powerful analytical tool for solving the SIR Epidemic Model.
• This closed-form solution offers a more precise understanding of epidemic dynamics compared to purely numerical methods.
• The approach has significant implications for epidemiological research and pandemic response planning.