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Dynamics of SEIR epidemic model by optimal auxiliary functions method
Bogdan Marinca1, Vasile Marinca1,2, Ciprian Bogdan3,4
1Politehnica University of Timișoara, 300006, Timișoara, Romania.
Chaos, Solitons, and Fractals
|May 17, 2021
Summary
This study presents an approximate analytical solution for the COVID-19 Susceptible, Exposed, Infected, Recovered (SEIR) model. The Optimal Auxiliary Functions Method (OAFM) provides a fast and efficient approach for analyzing epidemic dynamics.
Area of Science:
- Epidemiology
- Mathematical Biology
- Computational Science
Background:
- The COVID-19 pandemic necessitates robust mathematical models for understanding disease transmission.
- Nonlinear Susceptible, Exposed, Infected, Recovered (SEIR) models are crucial for simulating infectious disease dynamics.
- Developing efficient analytical solutions for these complex models is essential for accurate prediction and control.
Purpose of the Study:
- To establish an approximate analytical solution for the nonlinear SEIR model applied to COVID-19.
- To demonstrate the efficacy of the Optimal Auxiliary Functions Method (OAFM) for solving complex differential equations.
- To provide a computationally efficient method for analyzing COVID-19 epidemiological data.
Main Methods:
- Application of the Optimal Auxiliary Functions Method (OAFM) to a system of five nonlinear differential equations representing the SEIR model.
- Utilizing auxiliary functions and optimal convergence-control parameters within the OAFM framework.
- Ensuring the method's independence from small or large parameters in governing equations and initial/boundary conditions.
Main Results:
- Achieved an approximate analytical solution for the nonlinear COVID-19 SEIR model.
- Demonstrated rapid convergence of solutions, often after a single iteration.
- Validated the effectiveness, simplicity, and high efficiency of the OAFM.
Conclusions:
- The OAFM offers a powerful and efficient tool for obtaining approximate analytical solutions to nonlinear epidemiological models like the COVID-19 SEIR model.
- The method's fast convergence and independence from parameter size make it highly applicable for real-world epidemic analysis.
- This approach facilitates a deeper understanding of COVID-19 transmission dynamics and aids in public health strategy development.
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