Marchuk's model of immune system dynamics with application to tumour growth

Journal of Theoretical Medicine

Volumn 4, Issue 1, 2002, Pages 85-93

  Foryś, Urszula ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

Antibody; Antigen; Delay differential equation; Hopf bifurcation; Humoral and cellular immune response; Local and global stability; Plasma cell

Indexed keywords

ANTIBODY; ANTIGEN; CYTOKINE;

ADAPTATION; ARTICLE; CANCER IMMUNOTHERAPY; CELL INTERACTION; COMPUTER SIMULATION; CONTROLLED STUDY; IMMUNE SYSTEM; IMMUNOREACTIVITY; MATHEMATICAL MODEL; OSCILLATION; OUTCOMES RESEARCH; TUMOR CELL; TUMOR GROWTH; TUMOR IMMUNITY;

EID: 0036244827     PISSN: 10273662     EISSN: None     Source Type: Journal    
DOI: 10.1080/10273660290052151     Document Type: Article

References (26)

1. Disease dynamics
2. Immunological barrier for infectious diseases
3. Analysis of Mathematical Models in Immunology
4. A Model of the Immune System with Time-Dependent Immune Reactivity
5. "Behaviour of Marchuk's model depending on time delay"
6. "Periodic dynamics in the model of immune system"
7. The Marchuk's Model in the Case of Vaccination. Qualitative Behaviour and Some Applications
8. "A mathematical model of antibody concentration decline after vaccination for hepatitis B"
9. "Mathematical model of an immune system with random time of reaction"
10. "Discrete mathematical model of an immune system"
11. "Interleukin mathematical model of an immune system"
12. "Global analysis of Marchuk's model in a case of weak immune system"
13. "Global analysis of the initial value problem for a system of ODE modeling the immune system after vaccinations"
14. "Global analysis of Marchuk's model in case of strong immune system"
15. "A model of the immune system after vaccinations"
16. "Complementary analysis of the initial value problem for a system of ODE modelling immune system after vaccinations"
17. "Kinetics of hepatitis B vaccine-induced anti-HBs antibodies during an 82 month post-booster period"
18. "Quantification of hepatitis B vaccine-induced antibodies as a predictor of anti-HBs persistence"
19. Numerical methods for delay differential equations - Application of i-smooth calculus
20. "Modeling immunotherapy of the tumor-immune reaction"
21. "Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis"
22. Mathematical models in immunology
23. Mathematical Models in Immunology
24. Mathematical Modelling of Immune Response in Infectious Diseases
25. "A basic mathematical model of the immune response"
26. Some Remarks on Marchuk's Mathematical Model of Immune System