This model by Baker M. 2013, describesthe interaction between pro and anti-inflammatory cytokinesignalling in rheumatoid arthritis.

Using two ordinary differential equations, the first model [BIOMD0000000550]analyses bifurcation and describes different pathological states byaltering inflammatory regulation parameters.
The second model [BIOMD0000000549]includes the effect that ageing has on pro-inflammatory signalling,allowing for time-dependant properties and disease progression tobe observed. The author also describes potential dosing forreversal of the disease state.

This model is described in the article:

Mathematical modelling of cytokine-mediated inflammation in rheumatoid arthritis.

Baker M, Denman-Johnson S, Brook BS, Gaywood I, Owen MR.

Math Med Biol 2013 Dec; 30(4): 311-337

Abstract:

Rheumatoid arthritis (RA) is a chronic inflammatory disease preferentially affecting the joints and leading, if untreated, to progressive joint damage and disability. Cytokines, a group of small inducible proteins, which act as intercellular messengers, are key regulators of the inflammation that characterizes RA. They can be classified into pro-inflammatory and anti-inflammatory groups. Numerous cytokines have been implicated in the regulation of RA with complex up and down regulatory interactions. This paper considers a two-variable model for the interactions between pro-inflammatory and anti-inflammatory cytokines, and demonstrates that mathematical modelling may be used to investigate the involvement of cytokines in the disease process. The model displays a range of possible behaviours, such as bistability and oscillations, which are strongly reminiscent of the behaviour of RA e.g. genetic susceptibility and remitting-relapsing disease. We also show that the dose regimen as well as the dose level are important factors in RA treatments.