A Fast Second-Order Explicit Predictor-Corrector Numerical Technique To Investigating And Predicting The Dynamic Of Cytokine Levels And Human Immune Cells Activation In Response To Gram-Positive Bacteria: Staphylococcus Aureus

TL;DR

This paper introduces a second-order explicit predictor-corrector numerical method to efficiently simulate cytokine dynamics and immune cell activation in response to S. aureus infection, improving computational speed and stability.

Contribution

The paper presents a novel second-order explicit predictor-corrector algorithm specifically designed for coupled cellular-cytokine immune response models, enhancing accuracy and efficiency.

Findings

The method is at least zero-stable and second-order accurate.

Numerical experiments demonstrate faster and more efficient performance compared to existing schemes.

Simulations reveal detailed immune response dynamics to S. aureus infection.

Abstract

This paper develops a second-order explicit predictor-corrector numerical approach for solving a mathematical model on the dynamic of cytokine expressions and human immune cell activation in response to the bacterium staphylococcus aureus (S. aureus). The proposed algorithm is at least zero-stable and second-order accurate. Mathematical modeling works that analyze the human body in response to some antigens have predicted concentrations of a broad range of cells and cytokines. This study deals with a coupled cellular-cytokine model which predicts cytokine expressions in response to gram-positive bacteria S. aureus. Tumor necrosis factor alpha, interleukin 6, interleukin 8 and interleukin 10 are included to assess the relationship between cytokine release from macrophages and the concentration of the S. aureus antigen. Ordinary differential equations are used to model cytokine levels while the cellular responses are modeled by partial differential equations. Interactions between both components provide a more robust and complete systems of immune activation. In the numerical simulations, a low concentration of S. aureus is used to measure cellular activation and cytokine expressions. Numerical experiments indicate how the human immune system responds to infections from different pathogens. Furthermore, numerical examples suggest that the new technique is faster and more efficient than a large class of statistical and numerical schemes discussed in the literature for systems of nonlinear equations and can serve as a robust tool for the integration of general systems of initial-boundary value problems.