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Fractional methicillin-resistant Staphylococcus aureus infection model under Caputo operator
Bahar Acay1, Mustafa Inc1,2, Amir Khan3
1Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkey.
Journal of Applied Mathematics & Computing
|February 22, 2021
Summary
This study analyzes community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA) and hospital-acquired methicillin-resistant Staphylococcus aureus (HA-MRSA) transmission dynamics using fractional calculus. The research confirms disease-free equilibrium stability under specific conditions and identifies key parameters for infection control.
Area of Science:
- Mathematical modeling of infectious diseases
- Fractional calculus applications in epidemiology
- Microbiology and public health
Background:
- Methicillin-resistant Staphylococcus aureus (MRSA) poses a significant global health threat, causing more deaths annually than AIDS.
- Distinguishing between community-acquired (CA-MRSA) and hospital-acquired (HA-MRSA) strains is crucial for effective control strategies.
- Understanding transmission dynamics is essential to predict and manage MRSA outbreaks.
Purpose of the Study:
- To analyze the transmission dynamics between CA-MRSA and HA-MRSA using a Caputo fractional operator.
- To establish the existence, uniqueness, and stability of solutions for the fractional staph infection model.
- To identify critical parameters influencing MRSA spread through sensitivity analysis.
Main Methods:
- Application of the Caputo fractional derivative to model MRSA transmission.
- Utilizing fixed-point theorems to demonstrate the existence and uniqueness of model solutions.
- Employing stability analysis and the Laplace-Adomian decomposition method for iterative solutions.
- Parameterization using data from Beth Israel Deaconess Medical Center.
Main Results:
- The study proves the existence and uniqueness of solutions for the fractional staph infection model.
- Disease-free equilibrium is globally asymptotically stable when key parameters are less than one.
- Sensitivity analysis highlights parameters most influential in controlling MRSA spread.
- Simulations using various fractional orders demonstrate model behavior.
Conclusions:
- Fractional calculus provides a robust framework for analyzing complex infectious disease dynamics, including MRSA.
- The model offers insights into the competition between CA-MRSA and HA-MRSA, aiding in targeted interventions.
- Identifying sensitive parameters is vital for developing effective public health strategies to curb MRSA infections.
