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Subcutaneous Infection of Methicillin Resistant Staphylococcus Aureus MRSA
Published on: February 9, 2011
Fractional order model of MRSA bacterial infection with real data fitting: Computational Analysis and Modeling
Muhammad Farman1, Nezihal Gokbulut2, Ulas Hurdoganoglu3
1Faculty of Arts and Sciences, Department of Mathematics, Near East University, Nicosia, North Cyprus, 99138, Turkey; Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
Abstract:
Bacterial infections in the health-care sector and social environments have been linked to the Methicillin-Resistant Staphylococcus aureus (MRSA) infection, a type of bacteria that has remained an international health risk since the 1960s. From mild colonization to a deadly invasive disease with an elevated mortality rate, the illness can present in many different forms. A fractional-order dynamic model of MRSA infection developed using real data for computational and modeling analysis on the north side of Cyprus is presented in this paper. Initially, we tested that the suggested model had a positively invariant region, bounded solutions, and uniqueness for the biological feasibility of the model. We study the equilibria of the model and assess the expression for the most significant threshold parameter, called the basic reproduction number (ℛ0). The reproductive number's parameters are also subjected to sensitivity analysis through mathematical methods and simulations. Additionally, utilizing the power law kernel and the fixed-point approach, the existence, uniqueness, and generalized Ulam-Hyers-Rassias stability are presented. Chaos Control was used to regulate the linear responses approach to bring the system to stabilize according to its points of equilibrium, taking into account a fractional-order system with a managed design where solutions are bound in the feasible domain. Finally, numerical simulations demonstrating the effects of different parameters on MRSA infection are used to investigate the impact of the fractional operator on the generalized form of the power law kernel through a two-step Newton polynomial method. The impact of fractional orders is emphasized in the study so that the numerical solutions support the importance of these orders on MRSA infection. With the application of fractional order, the significance of cognizant antibiotic usage for MRSA infection is verified.
Insights
This study introduces a fractional-order dynamic model for Methicillin-Resistant Staphylococcus aureus (MRSA) infection, validating its stability and analyzing key parameters. The findings emphasize the importance of fractional calculus in understanding MRSA dynamics and guiding antibiotic use.
Area of Science:
- Mathematical Biology
- Infectious Disease Modeling
- Fractional Calculus
Background:
- Methicillin-Resistant Staphylococcus aureus (MRSA) poses a significant international health risk, presenting diverse clinical manifestations from colonization to severe invasive disease.
- Understanding the transmission dynamics and developing effective control strategies for MRSA are crucial in healthcare and social settings.
Purpose of the Study:
- To develop and analyze a novel fractional-order dynamic model for MRSA infection using real-world data.
- To investigate the biological feasibility, stability, and key epidemiological parameters of the proposed MRSA model.
- To explore the influence of fractional calculus on MRSA infection dynamics and antibiotic treatment strategies.
Main Methods:
- Development of a fractional-order dynamic model for MRSA infection.
- Analysis of model properties including invariant regions, bounded solutions, and uniqueness.
- Calculation and sensitivity analysis of the basic reproduction number (ℛ₀).
- Application of fixed-point theory for existence, uniqueness, and Ulam-Hyers-Rassias stability.
- Implementation of Chaos Control for system stabilization.
- Numerical simulations using a two-step Newton polynomial method to assess the impact of fractional orders.
Main Results:
- The fractional-order MRSA model was demonstrated to be biologically feasible with a positively invariant region and bounded solutions.
- The basic reproduction number (ℛ₀) was determined, and its parameters were analyzed for sensitivity.
- The existence, uniqueness, and generalized Ulam-Hyers-Rassias stability of the model were established.
- Numerical simulations confirmed the significant impact of fractional orders on MRSA infection dynamics.
- The study verified the importance of judicious antibiotic usage in managing MRSA infections through the lens of fractional calculus.
Conclusions:
- Fractional-order modeling provides a valuable framework for understanding the complex dynamics of MRSA infections.
- The analysis highlights the critical role of fractional orders in predicting infection spread and evaluating control measures.
- The findings underscore the necessity of informed antibiotic stewardship to combat the persistent threat of MRSA.
