A model of the immune system after vaccinations


The mathematical model of human immune reactions following a series of vaccinations (against hepatitis B) is proposed. The model is presented in terms of a functional-differential equation. Fundamental properties of the model are studied. Theoretical results derived from this model are compared with experimental data.

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  1. Belykh LN (1988) Analysis of mathematical models in immunology, (in Russian) Nauka, Moscow

    Google Scholar 

  2. Borkowska A, Szlenk W (1995) A mathematical model of antibody concentrations decline after vaccination for hepatitis B. Pol J Immunol 20: 117–122

    Google Scholar 

  3. Foryś U (1997) Global analysis of Marchuk’s model in a case of weak immune system. Math Comput Model 25: 97–106

    Google Scholar 

  4. Gesemann M, Scheiermann N (1993) Kinetics of hepatitis B vaccineinduced anti-Hbs antibodies during 82 month post-booster period. Proc Int Symp Viral and liver disease, Tokyo, Abs 244

  5. Hall AJ (1994) Immunization against viral hepatitis type B: how long protection and against what? Brit Med IV: 7–8

    Google Scholar 

  6. Madaliński K (1995) Vaccination against hepatitis B — current status and perspectives. Pol J Immunol 20: 3–15.

    Google Scholar 

  7. Marchuk GI (1980) Mathematical models in immunology (in Russian) Nauka, Moscow

    Google Scholar 

  8. Marchuk GI (1983) Mathematical models in immunology. Optimization Software INC, Publication Division, New York

    Google Scholar 

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Correspondence to U. Foryś.

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Foryś, U., Żołek, N. A model of the immune system after vaccinations. ARI 50, 180–184 (1998). https://doi.org/10.1007/s007770050012

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Key words

  • Functional-differential equation
  • Antigen
  • Antibody
  • Plasma cell
  • Organ-target