Fractional dynamic system simulating the growth of microbe

Area of Science:

• Mathematical Biology
• Infectious Disease Modeling
• Fractional Calculus

Background:

• Microbe growth dynamics are crucial for understanding disease spread.
• Existing models may not fully capture the complexities of infection diffusion.
• Fractional calculus offers a novel framework for dynamic system analysis.

Purpose of the Study:

• To simulate microbe growth using fractional calculus.
• To investigate a fractional system of integro-differential equations for infection dynamics.
• To assess the applicability of the model in distinguishing infection growth levels.

Main Methods:

• Utilizing fractional calculus, specifically the Atangana-Baleanu calculus (ABC).
• Developing a fractional system of integro-differential equations to model diffusion between infected and asymptomatic cases.
• Employing fractional Tutte polynomials for numerical solutions and simulation mapping.

Main Results:

• The proposed fractional system effectively simulates microbe growth dynamics.
• The model accurately distinguishes between different levels of infection growth.
• The mechanism of infection spread was validated as positively active.

Conclusions:

• Fractional calculus provides a powerful tool for modeling complex biological systems like infection spread.
• The Atangana-Baleanu calculus based model offers a robust method for analyzing infectious disease dynamics.
• The study demonstrates the practical utility of the proposed methodology with real data.