TY - JOUR
T1 - Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates
AU - Enatsu, Yoichi
AU - Messina, Eleonora
AU - Nakata, Yukihiko
AU - Muroya, Yoshiaki
AU - Russo, Elvira
AU - Vecchio, Antonia
N1 - Funding Information:
Acknowledgements The authors wish to express their gratitude to the editor and an anonymous referee for very helpful comments and valuable suggestion 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 third author, and by Scientific Research (c), No. 21540230 of Japan Society for the Promotion of Science to the fourth author.
PY - 2012/6
Y1 - 2012/6
N2 - In this paper, by constructing Lyapunov functionals, we consider the global dynamics of an SIRS epidemic model with a wide class of nonlinear incidence rates and distributed delays ∫ h 0 p(τ)f(S(t),I(t- τ))dτ under the condition that the total population converges to 1. By using a technical lemma which is derived from strong condition of strict monotonicity of functions f(S,I) and f(S,I)/I with respect to S≥0 and I>0, we extend the global stability result for an SIR epidemic model if R 0>1, where R 0 is the basic reproduction number. By using a limit system of the model, we also show that the disease-free equilibrium is globally asymptotically stable if R 0=1.
AB - In this paper, by constructing Lyapunov functionals, we consider the global dynamics of an SIRS epidemic model with a wide class of nonlinear incidence rates and distributed delays ∫ h 0 p(τ)f(S(t),I(t- τ))dτ under the condition that the total population converges to 1. By using a technical lemma which is derived from strong condition of strict monotonicity of functions f(S,I) and f(S,I)/I with respect to S≥0 and I>0, we extend the global stability result for an SIR epidemic model if R 0>1, where R 0 is the basic reproduction number. By using a limit system of the model, we also show that the disease-free equilibrium is globally asymptotically stable if R 0=1.
KW - Global asymptotic stability
KW - Lyapunov functional
KW - Nonlinear incidence rate
KW - SIRS epidemic model
UR - https://www.scopus.com/pages/publications/84860338947
U2 - 10.1007/s12190-011-0507-y
DO - 10.1007/s12190-011-0507-y
M3 - Article
AN - SCOPUS:84860338947
SN - 1598-5865
VL - 39
SP - 15
EP - 34
JO - Journal of Applied Mathematics and Computing
JF - Journal of Applied Mathematics and Computing
IS - 1-2
ER -