Analysis of COVID-19 epidemic model with sumudu transform

Area of Science:

• Mathematical modeling
• Epidemiology
• Fractional calculus

Background:

• The COVID-19 pandemic necessitates robust mathematical models for understanding disease spread.
• Quarantine measures significantly impact disease transmission dynamics.
• Fractional calculus offers advanced tools for modeling complex phenomena like disease spread.

Purpose of the Study:

• To develop and analyze a time-fractional COVID-19 model that includes the effects of quarantine.
• To investigate the application of the Atangana-Baleanu-Caputo (ABC) technique and Sumudu transform in fractional modeling of infectious diseases.
• To explore the influence of various fractional parameters on disease dynamics during quarantine.

Main Methods:

• Development of a system of fractional differential equations for the COVID-19 model.
• Application of the Atangana-Baleanu-Caputo (ABC) derivative and Sumudu transform.
• Utilizing fixed-point theory to establish the existence and uniqueness of solutions.
• Numerical analysis of the model with different fractional orders.

Main Results:

• The study successfully derived solutions for the fractional-order COVID-19 model.
• The analysis demonstrated the significant impact of the fractional operator on disease dynamics during quarantine.
• The properties of the Sumudu transform were leveraged for effective analysis.

Conclusions:

• The developed fractional-order model provides a valuable framework for understanding COVID-19 spread under quarantine.
• Fractional calculus, particularly with the ABC technique and Sumudu transform, offers powerful insights into epidemiological dynamics.
• The findings highlight the importance of considering fractional dynamics in public health interventions during pandemics.