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Published on: June 4, 2012
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.
Abstract:
This study provides a detailed exposition of in-hospital community-acquired methicillin-resistant S. aureus (CA-MRSA) which is a new strain of MRSA, and hospital-acquired methicillin-resistant S. aureus (HA-MRSA) employing Caputo fractional operator. These two strains of MRSA, referred to as staph, have been a serious problem in hospitals and it is known that they give rise to more deaths per year than AIDS. Hence, the transmission dynamics determining whether the CA-MRSA overtakes HA-MRSA is analyzed by means of a non-local fractional derivative. We show the existence and uniqueness of the solutions of the fractional staph infection model through fixed-point theorems. Moreover, stability analysis and iterative solutions are furnished by the recursive procedure. We make use of the parameter values obtained from the Beth Israel Deaconess Medical Center. Analysis of the model under investigation shows that the disease-free equilibrium existing for all parameters is globally asymptotically stable when both and are less than one. We also carry out the sensitivity analysis to identify the most sensitive parameters for controlling the spread of the infection. Additionally, the solution for the above-mentioned model is obtained by the Laplace-Adomian decomposition method and various simulations are performed by using convenient fractional-order .
Insights
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.
