Toward an efficient approximate analytical solution for 4-compartment COVID-19 fractional mathematical model

Area of Science:

• Mathematical modeling
• Epidemiology
• Fractional calculus

Background:

• The COVID-19 pandemic necessitates accurate predictive models.
• Existing models may not fully capture disease dynamics.
• Fractional calculus offers advanced analytical tools.

Purpose of the Study:

• To propose and analyze a time-fractional SEIR model for COVID-19 in China.
• To apply the multistage optimal homotopy asymptotic method (MOHAM) for an approximate analytical solution.
• To investigate the impact of vaccination on COVID-19 spread.

Main Methods:

• Development of a time-fractional SEIR mathematical model for COVID-19.
• Application of the multistage optimal homotopy asymptotic method (MOHAM) for solving the fractional model.
• Analysis of equilibrium points and basic reproduction number (R0).
• Local stability analysis of the model.
• Utilizing World Health Organization data for validation.
• Implementation using Maple software.

Main Results:

• The study provides a novel closed-form series solution for the fractional COVID-19 model.
• Analysis indicates a decreasing trend in the infected population until October 14, 2021.
• Vaccination is predicted to cause a further slight decrease in infections.
• The performance and behavior of various fractional orders of the model are presented graphically and in tables.

Conclusions:

• The fractional-order SEIR model with MOHAM is effective for predicting COVID-19 dynamics.
• Fractional calculus provides a valuable framework for epidemiological modeling.
• The findings support the continued importance of vaccination in controlling the pandemic.