Abstract
We analyse, from a mathematical point of view, the global stability of equilibria for models describing the interaction between infectious agents and humoral immunity. We consider the models that contain the variables of pathogens explicitly. The first model considers the situation where only a single strain exists. For the single strain model, the disease steady state is globally asymptotically stable if the basic reproductive ratio is greater than one. The other models consider the situations where multiple strains exist. For the multi-strain models, the disease steady state is globally asymptotically stable. In the model that does not explicitly contain an immune variable, only one strain with the maximum basic reproductive ratio can survive at the steady state. However, in our models explicitly involving the immune system, multiple strains coexist at the steady state.
| Original language | English |
|---|---|
| Pages (from-to) | 282-295 |
| Number of pages | 14 |
| Journal | Journal of Biological Dynamics |
| Volume | 4 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - May 2010 |
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Keywords
- Global stability
- Humoral immunity
- Lasalle's invariance principle
- Lyapunov function
- Multiple strains
ASJC Scopus subject areas
- Ecology, Evolution, Behavior and Systematics
- Ecology
Cite this
Global stability of models of humoral immunity against multiple viral strains. / Inoue, Toru; Kajiwara, Tsuyoshi; Sasaki, Toru.
In: Journal of Biological Dynamics, Vol. 4, No. 3, 05.2010, p. 282-295.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Global stability of models of humoral immunity against multiple viral strains
AU - Inoue, Toru
AU - Kajiwara, Tsuyoshi
AU - Sasaki, Toru
PY - 2010/5
Y1 - 2010/5
N2 - We analyse, from a mathematical point of view, the global stability of equilibria for models describing the interaction between infectious agents and humoral immunity. We consider the models that contain the variables of pathogens explicitly. The first model considers the situation where only a single strain exists. For the single strain model, the disease steady state is globally asymptotically stable if the basic reproductive ratio is greater than one. The other models consider the situations where multiple strains exist. For the multi-strain models, the disease steady state is globally asymptotically stable. In the model that does not explicitly contain an immune variable, only one strain with the maximum basic reproductive ratio can survive at the steady state. However, in our models explicitly involving the immune system, multiple strains coexist at the steady state.
AB - We analyse, from a mathematical point of view, the global stability of equilibria for models describing the interaction between infectious agents and humoral immunity. We consider the models that contain the variables of pathogens explicitly. The first model considers the situation where only a single strain exists. For the single strain model, the disease steady state is globally asymptotically stable if the basic reproductive ratio is greater than one. The other models consider the situations where multiple strains exist. For the multi-strain models, the disease steady state is globally asymptotically stable. In the model that does not explicitly contain an immune variable, only one strain with the maximum basic reproductive ratio can survive at the steady state. However, in our models explicitly involving the immune system, multiple strains coexist at the steady state.
KW - Global stability
KW - Humoral immunity
KW - Lasalle's invariance principle
KW - Lyapunov function
KW - Multiple strains
UR - http://www.scopus.com/inward/record.url?scp=79955918721&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79955918721&partnerID=8YFLogxK
U2 - 10.1080/17513750903180275
DO - 10.1080/17513750903180275
M3 - Article
VL - 4
SP - 282
EP - 295
JO - Journal of Biological Dynamics
JF - Journal of Biological Dynamics
SN - 1751-3758
IS - 3
ER -