Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates
View/ Open
Date
2012-12-31Author
Enatsu Y.
Messina E.
Nakata Y.
Muroya Y.
Russo E.
Vecchio A.
Metadata
Show full item recordAbstract
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.