Global analysis of the initial value problem for a system of O.D.E. modeling the immune system after vaccinations

Mathematical and Computer Modelling

Volumn 29, Issue 3, 1999, Pages 79-85

  Forys U ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

Antibody; Antigen; Delay differential equation; Plasma cell

Indexed keywords

EID: 0033082762     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(99)00031-X     Document Type: Article

References (11)

1. U. Foryś and N. Zolek. A model of immune system after vaccinations, ARI (to appear).
2. G.I. Marchuk, Mathematical Models in Immunology, Optimization Software INC, Publication Division, New York, (1983).
3. L.N. Belykh, Analysis of Mathematical Models in Immunology, (in Russian), Nauka, Moscow, (1988).
4. A.J. Hall, Immunization against viral hepatitis type B: How long protection and against what?, Brit. Med. IV, 7-8, (1994).
5. K. Madaliński, Vaccination against hepatitis B - Current status and perspectives, Pol. J. Immunology 20, 3-15, (1995).
6. A. Borkowska and W. Szlenk, A mathematical model of antibody concentrations decline after vaccination for hepatitis B, Pol. J. Immunology 20, 117-122, (1995).
7. J.D. Murray, Lectures on noninear-diff-equation, in Models in Biology, Clarendon Press, Oxford, (1977).
8. M. Peschel and W. Mende, The Predator-Prey Model: Do We Live in a Volterra World?, Akademie-Verlag, Berlin, (1986).
9. J. Hale and H. Kocak, Dynamics and Bifurcations, Springer, New York, (1991).
10. F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, Springer, Berlin, (1990).
11. W. Szlenk, An Introduction to the Theory of Smooth Dynamical Systems, PWN/John Wiley & Sons, Warsaw/Chichester, (1984).