Dynamical Model of Cytokines in Rheumatoid Arthritis in the Presence of Additive Noise

A dynamical model from Baker et. al* is used to explore the possibility of predicting onset of Rheumatoid Arthritis. The model is based on nonlinear interaction of pro- inflammatory and anti-inflammatory cytokines. In the model, a parameter measures the effect of the pro-inflammatory cytokine concentration on further growth of pro- inflammatory cytokines. As this parameter increases, a healthy state jumps to a disease state through a fold bifurcation. By adding noise to the model, we observe precursor flickering and large-scale fluctuations that might appear clinically as early clues to incipient onset.
*M. Baker, S. Denman-Johnson, and M. R. Owen, “Mathematical modelling of cytokine-mediated inflammation in rheumatoid arthritis” Mathematical Medicine and Biology (2013) 30, 311–337)