Abstract
The stability analysis of the interior equilibria, whose components are all positive, of non linear ordinary differential equation models describing in vivo dynamics of infectious diseases are complicated in general. Liu, "Non-linear oscillation in models of immune responses to persistent viruses, Theor. Popul. Biol. 52(1997), 224-230" and Murase, Sasaki and Kajiwara, "Stability analysis of pathogen-immune interaction dynamics (submitted)" proved the stability of the interior equilibria of such models using symbolic calculation software on computers. In this paper, proofs without using symbolic calculation software of the stability theorems given by Liu and Murase et al. are presented. Simple algebraic manipulations, properties of determinants, and their derivatives are used. The details of the calculation given by symbolic calculation software can be seen clearly.
| Original language | English |
|---|---|
| Pages (from-to) | 615-622 |
| Number of pages | 8 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 4 |
| Issue number | 3 |
| Publication status | Published - Aug 2004 |
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Keywords
- Differential equation
- Immune response
- Infectious diseases
- Stability
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
- Discrete Mathematics and Combinatorics
Cite this
A note on the stability analysis of pathogen-immune interaction dynamics. / Kajiwara, Tsuyoshi; Sasaki, Toru.
In: Discrete and Continuous Dynamical Systems - Series B, Vol. 4, No. 3, 08.2004, p. 615-622.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A note on the stability analysis of pathogen-immune interaction dynamics
AU - Kajiwara, Tsuyoshi
AU - Sasaki, Toru
PY - 2004/8
Y1 - 2004/8
N2 - The stability analysis of the interior equilibria, whose components are all positive, of non linear ordinary differential equation models describing in vivo dynamics of infectious diseases are complicated in general. Liu, "Non-linear oscillation in models of immune responses to persistent viruses, Theor. Popul. Biol. 52(1997), 224-230" and Murase, Sasaki and Kajiwara, "Stability analysis of pathogen-immune interaction dynamics (submitted)" proved the stability of the interior equilibria of such models using symbolic calculation software on computers. In this paper, proofs without using symbolic calculation software of the stability theorems given by Liu and Murase et al. are presented. Simple algebraic manipulations, properties of determinants, and their derivatives are used. The details of the calculation given by symbolic calculation software can be seen clearly.
AB - The stability analysis of the interior equilibria, whose components are all positive, of non linear ordinary differential equation models describing in vivo dynamics of infectious diseases are complicated in general. Liu, "Non-linear oscillation in models of immune responses to persistent viruses, Theor. Popul. Biol. 52(1997), 224-230" and Murase, Sasaki and Kajiwara, "Stability analysis of pathogen-immune interaction dynamics (submitted)" proved the stability of the interior equilibria of such models using symbolic calculation software on computers. In this paper, proofs without using symbolic calculation software of the stability theorems given by Liu and Murase et al. are presented. Simple algebraic manipulations, properties of determinants, and their derivatives are used. The details of the calculation given by symbolic calculation software can be seen clearly.
KW - Differential equation
KW - Immune response
KW - Infectious diseases
KW - Stability
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UR - http://www.scopus.com/inward/citedby.url?scp=2942692340&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:2942692340
VL - 4
SP - 615
EP - 622
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 3
ER -