TY - JOUR
T1 - Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model
AU - Enatsu, Yoichi
AU - Nakata, Yukihiko
AU - Muroya, Yoshiaki
N1 - Funding Information:
The authors wish to express their gratitude to the Editor and an anonymous referee for their helpful comments and valuable suggestions which improved the quality of this paper. The authors’ work was supported in part by JSPS Fellows, No. 237213 of Japan Society for the Promotion of Science to the first author, by the Grant MTM2010-18318 of the MICINN, Spanish Ministry of Science and Innovation to the second author, and by Scientific Research (c), No. 21540230 of Japan Society for the Promotion of Science to the third author. The work of this paper was partially prepared at Technische Universität Darmstadt from the beginning of October to the end of November 2011, participating in the International Research Training Group Mathematical Fluid Dynamics funded by Deutsche Forschungsgemeinschaft (DFG) and Japan Society for the Promotion of Science (JSPS).
PY - 2012/10
Y1 - 2012/10
N2 - In this paper, we study the global dynamics of a delayed SIRS epidemic model for transmission of disease with a class of nonlinear incidence rates of the form βS(t)∫ 0 hf(τ)G(I(t-τ))dτ. Applying Lyapunov functional techniques in the recent paper [Y. Nakata, Y. Enatsu, Y. Muroya, On the global stability of an SIRS epidemic model with distributed delays, Discrete Contin. Dyn. Syst. Supplement (2011) 11191128], we establish sufficient conditions of the rate of immunity loss for the global asymptotic stability of an endemic equilibrium for the model. In particular, we offer a unified construction of Lyapunov functionals for both cases of R 0 ≤ 1 and R 0 > 1, where R 0 is the basic reproduction number.
AB - In this paper, we study the global dynamics of a delayed SIRS epidemic model for transmission of disease with a class of nonlinear incidence rates of the form βS(t)∫ 0 hf(τ)G(I(t-τ))dτ. Applying Lyapunov functional techniques in the recent paper [Y. Nakata, Y. Enatsu, Y. Muroya, On the global stability of an SIRS epidemic model with distributed delays, Discrete Contin. Dyn. Syst. Supplement (2011) 11191128], we establish sufficient conditions of the rate of immunity loss for the global asymptotic stability of an endemic equilibrium for the model. In particular, we offer a unified construction of Lyapunov functionals for both cases of R 0 ≤ 1 and R 0 > 1, where R 0 is the basic reproduction number.
KW - Distributed delays
KW - Global asymptotic stability
KW - Lyapunov functional
KW - Nonlinear incidence rate
KW - SIRS epidemic model
UR - https://www.scopus.com/pages/publications/84859101715
U2 - 10.1016/j.nonrwa.2012.01.007
DO - 10.1016/j.nonrwa.2012.01.007
M3 - Article
AN - SCOPUS:84859101715
SN - 1468-1218
VL - 13
SP - 2120
EP - 2133
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
IS - 5
ER -