A KdV-SIR equation and its analytical solutions: An application for COVID-19 data analysis

Area of Science:

• Epidemiology
• Mathematical Biology
• Nonlinear Dynamics

Background:

• The classical SIR (Susceptible-Infected-Recovered) model is foundational for understanding epidemic dynamics.
• Describing the time evolution of infected individuals during epidemic waves requires advanced mathematical frameworks.
• Weakly nonlinear assumptions are often necessary to simplify complex epidemiological models.

Purpose of the Study:

• To derive and apply the KdV-SIR equation for estimating epidemic peak times.
• To assess the feasibility of using the KdV-SIR equation with COVID-19 data for peak time prediction.
• To propose and verify a novel prediction method for peak infection times.

Main Methods:

• Mathematical derivation of the KdV-SIR equation, analogous to the Korteweg-de Vries (KdV) equation.
• Generation of synthetic COVID-19 data using curve fitting, empirical mode decomposition (EMD), and a 28-day running mean.
• Application of derived formulas for ensemble forecasts and estimation of growth rates.

Main Results:

• The KdV-SIR equation provides analytical solutions applicable to epidemiological data.
• Ensemble forecasts using generated data yielded various estimates for epidemic peak times.
• The proposed method, reliant on a single parameter ($$), demonstrated a straightforward alternative for peak time estimation.

Conclusions:

• The KdV-SIR equation is a feasible tool for estimating epidemic peak times when combined with real-world data.
• The developed prediction method offers a simplified approach compared to other techniques.
• The study highlights the utility of nonlinear dynamics in epidemiological forecasting.