## Abstract

Rheumatoid arthritis is an autoimmune disease of unknown etiology that manifests as a persistent inammatory syn- ovitis and eventually destroys the joints. The immune system recognizes synovial cells as not self and consequently causes lymphocyte and antibody proliferation that is promoted by the pro-inammatory cytokines, the most significant being tumor necrosis factor TNF-. In the treatment of rheumatoid arthritis either monoclonal antibodies or soluble receptors are used to neutralize the TNF- bioactivity, such as sTNFR2, Etanercept and Iniximab. In [M. Jit et al. Rheumatology 2005;44:323- 331] a mathematical model that represents the TNF-dynamics in the inamed synovial joint within which locally produced TNF-_ can bind to cell-surface receptors was proposed. It consists of four coupled ordinary differential equations, that were integrated numerically assuming a range of estimates of the key parameters. In this paper we complement the previous work by determining the general solution of those equations for speci_c conditions on the parameters. Then we characterize the behavior of TNF- in the presence of different inhibitors and also evaluate the inhibitors effectiveness in the treatment of rheumatoid arthritis.