TY - JOUR
T1 - Global stability of a generalized epidemic model
AU - Iwami, Shingo
AU - Hara, Tadayuki
N1 - Funding Information:
The authors express thanks to Prof. Yasuhiro Takeuchi for valuable comments. Shingo was supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. Furthermore, we would like to thank anonymous referees for very helpful suggestions and comments which improved the quality of this paper and study.
PY - 2010/2/15
Y1 - 2010/2/15
N2 - The competitive exclusion principle is one of the most interesting and important phenomena in both theoretical epidemiology and biology. We show that the equilibrium in which only the strain with the maximum basic reproductive number exists is globally asymptotically stable by using an average Lyapunov function theorem and some dynamical system theory. This result is anticipated by H.J. Bremermann and H.R. Thieme (1989) [6] where they showed that the equilibrium is locally stable - the global result has not been established previously.
AB - The competitive exclusion principle is one of the most interesting and important phenomena in both theoretical epidemiology and biology. We show that the equilibrium in which only the strain with the maximum basic reproductive number exists is globally asymptotically stable by using an average Lyapunov function theorem and some dynamical system theory. This result is anticipated by H.J. Bremermann and H.R. Thieme (1989) [6] where they showed that the equilibrium is locally stable - the global result has not been established previously.
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U2 - 10.1016/j.jmaa.2009.07.059
DO - 10.1016/j.jmaa.2009.07.059
M3 - Article
AN - SCOPUS:70350346048
SN - 0022-247X
VL - 362
SP - 286
EP - 300
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -