<p>List of model variables.</p>

Tumour necrosis factor inhibitors, like adalimumab, are used to treat severe cases, but up to 25% of patients discontinue due to reduced effectiveness, often from emergence of anti-drug antibodies. Methotrexate, while ineffective alone in treatment, has shown potential in reducing the formation of anti-drug antibodies to the therapeutic compound, but its mechanism of action on the immune response remains unclear.

The objective of the study is to develop a mathematical model that describes the impact of methotrexate in reducing the immunogenicity of adalimumab in axial spondyloarthritis. Based on mathematical models established in the literature, we formulate a system of ordinary differential equations to describe the temporal dynamics of the immune cells (T and B lymphocytes), the therapeutic compounds in the study (adalimumab and methotrexate), and TNF.