On the Mathematical Model of Drug Treatment of Rheumatoid Arthritis

  • Kakha OdishariaEmail author
  • Vladimer Odisharia
  • Paata Tsereteli
  • Nona Janikashvili
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 276)


The model based investigation of immune mediated disorders is a complex and evolving field. We herein report about further development of the mathematical model of rheumatoid arthritis. We improved previously reported model (Odisharia et al. in Vekua Inst Appl Math 31:107–110, 2017, [1]) by providing treatment component. Tocilizumab is considered as a drug for treatment. The model explores the functional dynamics of cartilage destruction during disease progression, in which a model deciphers the interactions between B and T lymphocytes. Coefficients of model equations allow the adaptation of the model to an individual case of patients that is its advantage. These coefficients can be calculated automatically based on the results of blood clinical analysis. Developed software simulates treatment process which will help in process of choosing optimal treatment scheme.


Mathematical model of rheumatoid arthritis Drug therapy Coefficient estimation System of non-linear differential equations Optimal treatment scheme 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kakha Odisharia
    • 1
    Email author
  • Vladimer Odisharia
    • 2
  • Paata Tsereteli
    • 1
  • Nona Janikashvili
    • 3
  1. 1.St. Andrew the First-Called Georgian University of Patriarchate of GeorgiaTbilisiGeorgia
  2. 2.I.JavakhishviliTbilisi State UniversityTbilisiGeorgia
  3. 3.Tbilsi State Medical UniversityTbilisiGeorgia

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