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.
This is a preview of subscription content, access via your institution.
Belykh LN (1988) Analysis of mathematical models in immunology, (in Russian) Nauka, Moscow
Borkowska A, Szlenk W (1995) A mathematical model of antibody concentrations decline after vaccination for hepatitis B. Pol J Immunol 20: 117–122
Foryś U (1997) Global analysis of Marchuk’s model in a case of weak immune system. Math Comput Model 25: 97–106
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
Hall AJ (1994) Immunization against viral hepatitis type B: how long protection and against what? Brit Med IV: 7–8
Madaliński K (1995) Vaccination against hepatitis B — current status and perspectives. Pol J Immunol 20: 3–15.
Marchuk GI (1980) Mathematical models in immunology (in Russian) Nauka, Moscow
Marchuk GI (1983) Mathematical models in immunology. Optimization Software INC, Publication Division, New York
About this article
Cite this article
Foryś, U., Żołek, N. A model of the immune system after vaccinations. ARI 50, 180–184 (1998). https://doi.org/10.1007/s007770050012
- Functional-differential equation
- Plasma cell